The deal marks the first time that the radio station has struck a deal with Liverpool, making it something of a coup for the station's new owners UTV, which bought TalkSport's parent company The Wireless Group in May after a failed management buyout led by former Sun editor Kelvin MacKenzie.
The deals cover UEFA Champions League fixtures for all three clubs on a national basis as well as Premiership home games by Chelsea and Arsenal for London-only transmission.
Scott Taunton, chief executive of The Wireless Group, said: "There is no doubt that TalkSport listeners love our distinctive style of commentary -- which is passionate, lively and perfectly in tune with the terraces.
"Of course, we will continue to broadcast our incredibly popular Football First programme from noon to five on Saturday afternoons, which provides the ultimate in matchday coverage with reports from around the grounds across the country."
The deal follows TalkSport's signing of former England star and football pundit Rodney Marsh for the station's drivetime show at the start of the football season.
Marsh joins former footballers including Alan Brazil, Andy Townsend, Alvin Martin, Gary Stevens, Ray Houghton, Mick Quinn and Jason Cundy at the station.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the