Exhibit 23

CONSENT OF INDEPENDENT REGISTERED PUBLIC ACCOUNTING FIRM

We consent to the incorporation by reference in the registration statement (No. 333-74163) on Form S-3 and registration statements (No. 333-49912, 33-24415, 33-62541, 333-64661, 333-30528 and 333-105033) on Form S-8 of Sigma-Aldrich Corporation of our reports dated March 9, 2005 with respect to the consolidated balance sheets of Sigma Aldrich Corporation as of December 31, 2004 and 2003, and the related consolidated statements of income, stockholders’ equity and cash flows for each of the years in the three-year period ended December 31, 2004, management’s assessment of the effectiveness of internal control over financial reporting and the effectiveness of internal control over financial reporting as of December 31, 2004, which reports appear in the December 31, 2004 annual report on Form 10-K of Sigma-Aldrich Corporation.

/s/ KPMG LLP

St. Louis, Missouri

March 9, 2005