Norway forward King, 29, only joined the Blues in February on a deal until the end of the season.
Bolasie, 32, last played for the club in May 2018, while Besic's last appearance was in December 2017.
Bosnian midfielder Besic was the longest-serving player of the four but was restricted to just 56 appearances after joining the club from Ferencvaros in 2014.
On-loan goalkeeper Robin Olsen also leaves Merseyside to return to his parent club Roma.
The Sweden international made seven Premier League appearances last term having being brought in to provide competition for England number one Jordan Pickford.