Thomas S. Harman

+1.202.373.6725

thomas.harman@morganlewis.com

VIA EDGAR

March 12, 2019

U.S. Securities and Exchange Commission

100 F Street, NE

Washington, DC 20549

Re: Nuveen AMT-Free Municipal Value Fund (File Nos. 333-211789 and 811-22253)

Dear Sir or Madam:

On behalf of our client, Nuveen AMT-Free Municipal Value Fund (the “Fund”), we are filing, pursuant to Rule 497(j) under the Securities Act of 1933, as amended (the “1933 Act”), this letter certifying that the forms of Prospectus and Statement of Additional Information that would have been filed pursuant to Rule 497(c) under the 1933 Act would not have differed from those included as part of Post-Effective Amendment No. 3 to the Fund’s Registration Statement on Form N-2, which was filed electronically with the U.S. Securities and Exchange Commission via EDGAR Accession No. 0001193125-19-069045 on March 8, 2019.

Please do not hesitate to contact me at (202) 373-6725 should you have any questions.

Very truly yours,

/s/ Thomas S. Harman

Thomas S. Harman