Filed pursuant to Rule 497(e)

File Nos. 002-84012 and 811-03752

AMG FUNDS III

AMG Managers Cadence Capital Appreciation Fund

AMG Managers Cadence Emerging Companies Fund

Supplement dated March 20, 2017 to the

Prospectus, dated October 1, 2016, as revised October 27, 2016 and supplemented January 3, 2017 and February 27, 2017, and Statement of Additional Information, dated October 1, 2016, as supplemented January 3, 2017 and February 27, 2017

The following information supplements and supersedes any information to the contrary relating to AMG Managers Cadence Capital Appreciation Fund (the “Capital Appreciation Fund”) and AMG Managers Cadence Emerging Companies Fund (the “Emerging Companies Fund” and, together with the Capital Appreciation Fund, the “Funds”), each a series of AMG Funds III (the “Trust”), contained in the Funds’ Prospectus (the “Prospectus”) and Statement of Additional Information (“SAI”), dated, revised, and supplemented as noted above.

AMG Managers Cadence Capital Appreciation Fund

At a meeting held on March 15-16, 2017, the Board of Trustees of the Trust approved the reorganization of the Capital Appreciation Fund with and into AMG Renaissance Large Cap Growth Fund (the “Reorganization”), subject to the approval of shareholders of the Capital Appreciation Fund. If approved by the shareholders of the Capital Appreciation Fund, the Reorganization is expected to close on or about July 31, 2017, or as soon thereafter as practicable. Additional information about the Reorganization will be provided in the proxy solicitation materials for the Reorganization, which will be sent at a future date.

AMG Managers Cadence Emerging Companies Fund

Effective on or about June 1, 2017, the management fee for the Emerging Companies Fund will be reduced from 1.25% to 0.69%, the contractual expense limitation amount will be reduced from 1.42% to 0.89% (the terms of the Emerging Companies Fund’s expense limitation arrangement will otherwise remain the same) and Class I shares of the Emerging Companies Fund will be authorized to pay up to 0.10% in shareholder servicing fees. Shareholders will not experience any increase in expenses as a result of these changes as there will be no increase in the net expense ratio for the Emerging Companies Fund. AMG Funds LLC will pay a portion of the management fee to the Emerging Companies Fund’s subadviser for its services.

PLEASE KEEP THIS SUPPLEMENT FOR FUTURE REFERENCE

ST414