FILE NO. 333-
                                                                   CIK #1686055


                       SECURITIES AND EXCHANGE COMMISSION
                          Washington, D.C. 20549-1004

                             Registration Statement
                                       on
                                    Form S-6


     For Registration under the Securities Act of 1933 of Securities of Unit
Investment Trusts Registered on Form N-8B-2.

     A.   Exact name of Trust: INVESCO UNIT TRUSTS, TAXABLE INCOME SERIES 635

     B.   Name of Depositor: INVESCO CAPITAL MARKETS, INC.

     C.   Complete address of Depositor's principal executive offices:

                               11 Greenway Plaza
                           Houston, Texas 77046-1173

     D.   Name and complete address of agents for service:

PAUL HASTINGS LLP                              INVESCO CAPITAL MARKETS, INC.
Attention: Michael R. Rosella, Esq.            Attention: John M. Zerr, Esq.
200 Park Avenue                                11 Greenway Plaza
New York, New York  10166                      Houston, Texas 77046-1173

     E.   Title of securities being registered: Units of fractional undivided
          beneficial interest

     F.   Approximate date of proposed sale to the public:

                AS SOON AS PRACTICABLE AFTER THE EFFECTIVE DATE
                         OF THE REGISTRATION STATEMENT

     The registrant hereby amends this Registration Statement on such date or
dates as may be necessary to delay its effective date until the registrant shall
file a further amendment which specifically states that this Registration
Statement shall thereafter become effective in accordance with Section 8(a) of
the Securities Act of 1933 or until the Registration Statement shall become
effective on such date as the Commission, acting pursuant to said Section 8(a)
may determine.

                 Preliminary Prospectus Dated November 7, 2018

                 INVESCO UNIT TRUSTS, TAXABLE INCOME SERIES 635

     The attached final prospectus for a prior series of the Trust is hereby
used as a preliminary prospectus for the above stated series. The narrative
information and structure of the attached final prospectus will be substantially
the same as that of the final prospectus for this series. Information with
respect to pricing, the number of units, dates and summary information regarding
the characteristics of securities to be deposited in this series is not now
available and will be different since each series has a unique portfolio.
Accordingly, the information contained herein with regard to the previous series
should be considered as being included for informational purposes only. Ratings
of the securities in this series are expected to be comparable to those of the
securities deposited in the previous series. However, the Estimated Current
Return for this series will depend on the interest rates and offering prices of
the securities in this series and may vary materially from that of the previous
series.

     Information contained herein is subject to completion or amendment. Such
units may not be sold nor may an offer to buy be accepted prior to the time the
registration statement becomes effective. This prospectus shall not constitute
an offer to sell or the solicitation of an offer to buy nor shall there be any
sale of the units in any state in which such offer, solicitation or sale would
be unlawful prior to registration or qualification under the securities laws of
any such state.

     (Incorporated herein by reference is the final prospectus from Invesco Unit
Trusts, Taxable Income Series 597 (Registration No. 333-214003) as filed on
September 28, 2018, which shall be used as a preliminary prospectus for the
current series of the Trust.)

     The Securities and Exchange Commission has not approved or disapproved
these securities or passed upon the adequacy of this prospectus. Any
representation to the contrary is a criminal offense.

                       CONTENTS OF REGISTRATION STATEMENT

     This Registration Statement comprises the following papers and documents:

         The Facing Sheet of Form S-6.
         The Prospectus.
         The Signatures.
         The Written Consents of Legal Counsel, Evaluator and Independent
            Registered Public Accounting Firm.

     The following exhibits:

     1.1  Trust Agreement (to be supplied by amendment).

   1.1.1  Standard Terms and Conditions of Trust. Reference is made to Exhibit
          1.1.1 to the Registration Statement on Form S-6 of Invesco Unit
          Trusts, Taxable Income Series 429 (File No. 333-183830) dated December
          10, 2012.

     1.2  Certificate of Incorporation of Van Kampen Funds Inc. Reference is
          made to Exhibit 1.2 to the Registration Statement on Form S-6 of Van
          Kampen Focus Portfolios, Series 320 (File No. 333-75548) dated January
          2, 2002.

   1.2.1  Certificate of Amendment of Certificate of Incorporation changing the
          name of the Depositor to Invesco Capital Markets, Inc. Reference is
          made to Exhibit 1.2.1 to the Registration Statement on Form S-6 of
          Invesco Unit Trusts, Municipal Series 1130 (File No. 333-184264) dated
          December 4, 2012.

     1.3  By-laws of the Depositor. Reference is made to Exhibit 1.3 to the
          Registration Statement on Form S-6 of Van Kampen Focus Portfolios,
          Series 320 (File No. 333-75548) dated January 2, 2002.

     1.4  Form of Dealer Agreement. Reference is made to Exhibit 1.4 to the
          Registration Statement on Form S-6 of Van Kampen Unit Trusts,
          Municipal Series 560 (File No. 333-122799) dated May 18, 2005.

     1.5  Form of Master Agreement Among Underwriters. Reference is made to
          Exhibit 1.5 to the Registration Statement on Form S-6 of Van Kampen
          Unit Trusts, Municipal Series 560 (File No. 333-122799) dated May 18,
          2005.

     2.1  Form of Code of Ethics. Reference is made to Exhibit 2.1 to the
          Registration Statement on Form S-6 of Van Kampen Unit Trusts,
          Municipal Series 890 (File No. 333-165240) dated June 2, 2010.

     3.1  Opinion and Consent of Counsel as to the legality of securities being
          registered (to be supplied by amendment).

     3.3  Opinion of Counsel as to the Trustee and the Trust (to be supplied by
          amendment).

     4.1  Consent of Initial Evaluator (to be supplied by amendment).

     4.2  Consent of Independent Registered Public Accounting Firm (to be
          supplied by amendment).

     6.1  List of Officers and Directors of the Depositor. Reference is made to
          Exhibit 6.1 to the Registration Statement on Form S-6 of Invesco Unit
          Trusts, Series 1672 (File No. 333-212038) dated August 1, 2016.

     7.1  Powers of Attorney. Reference is made to Exhibit 7.1 to the
          Registration Statement on Form S-6 of Invesco Unit Trusts, Municipal
          Series 1130 (File No. 333-184264) dated December 4, 2012, and Invesco
          Unit Trusts, Series 1520 (File No. 333-201408) dated March 12, 2015.

                                   SIGNATURES

     Pursuant to the requirements of the Securities Act of 1933, the Registrant,
Invesco Unit Trusts, Taxable Income Series 635 has duly caused this Registration
Statement to be signed on its behalf by the undersigned, thereunto duly
authorized in the City of Chicago and State of Illinois on the 7th day of
November, 2018.

                                  INVESCO UNIT TRUSTS, TAXABLE INCOME SERIES 635
                                                                    (Registrant)

                                               By: INVESCO CAPITAL MARKETS, INC.
                                                                     (Depositor)


                                                         By: /s/ JOHN F. TIERNEY
                                                         -----------------------
                                                                  Vice President

     Pursuant to the requirements of the Securities Act of 1933, this
Registration Statement has been signed below on November 7, 2018, by the
following persons who constitute the principal officers and a majority of the
Board of Directors of Invesco Capital Markets, Inc.:

         SIGNATURE                            TITLE

Steven Massoni                           Director and Co-President

M. Kevin Cronin                          Director and Co-President

Mark W. Gregson                          Chief Financial Officer

                                                         By: /s/ JOHN F. TIERNEY
                                                         -----------------------
                                                             (Attorney-in-fact*)


---------------------
*    An executed copy of each of the related powers of attorney is filed
     herewith or incorporated herein by reference as set forth in Exhibit 7.1.