The length of the multi-year agreement was not disclosed.
ESPN will provide exclusive coverage of fights featuring Top Rank boxers on television and digital platforms.
ESPN will stream fights and other Top Rank content on the recently announced ESPN-branded direct-to-consumer streaming service via BAMTech and will also deliver selected pay-per-view events.
The broadcaster will show a total of 18 events in the first year of the partnership.
Creative Artists Agency (CAA) served as the media adviser to Top Rank on the agreement with ESPN.
The deal will begin with the Oscar Valdez v Gilberto Ramirez fight in Arizona on 22nd September.