Exhibit 23.1 Consent of Independent Registered Public Accounting Firm We consent to the incorporation by reference in Registration Statement No. 333-76399 of Accredo Health, Incorporated on Form S-8 of our report dated September 10, 2004, appearing in the Annual Report on Form 10-K of Accredo Health, Incorporated for the year ended June 30, 2004. /s/Deloitte & Touche LLP Memphis, Tennessee September 10, 2004