Hill, 38, and 32-year-old Senderos signed one-year deals last summer under Mark Warburton but neither is being retained as Pedro Caixinha looks to rebuild the squad he has inherited.
Hyndman's loan spell has been ended by injury.
He tweeted that he had enjoyed "an incredible time" at the Ibrox club.
The 21-year-old American arrived in January, along with Jon Toral on loan from Arsenal. He made 17 appearances and scored four goals.
Hill was one of 11 signings made by Warburton last summer, as the club prepared for its return to the top-flight.
The Englishman made 31 appearances, scoring six goals, including the equaliser in March's 1-1 draw at Celtic.
Former Arsenal defender Senderos was sent off on his debut in his team's 5-1 Old Firm defeat to Celtic back in September and made three further appearances.
Defenders Clint Hill and Philippe Senderos will leave Rangers at the end of the season while midfielder Emerson Hyndman has returned to Bournemouth.