
<PAGE>
 
                                                                    EXHIBIT 23.1


                         INDEPENDENT AUDITORS' CONSENT
                         -----------------------------


The Board of Directors
Evergreen Media Corporation:


We consent to incorporation by reference in the Registration Statements on Form
S-3 (No. 33-93874) and Form S-8 (Nos. 33-83124 and 333-04379) of Evergreen Media
Corporation, Inc. of our report dated June 28, 1996, relating to the balance
sheet of WEDR, Inc. as of December 31, 1995 and the related statements of
operations and retained earnings and cash flows for the year then ended, which
report appears in the Form 8-K dated August 23, 1996 filed by Evergreen Media
Corporation.



                                   KPMG Peat Marwick LLP


Dallas, Texas
August 19, 1996
