Chelsea's website said Remy was seeking a "fresh challenge" having spent last year on loan with Crystal Palace.
No fee was disclosed.
Former Olympique de Marseille striker Remy, 30, scored 12 goals in 47 appearances for the Blues and helped them win the Premier League title in 2014-15 under Jose Mourinho.
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Las Palmas lost both opening games in La Liga, scoring only once in the two games.
Argentine forward Sergio Araujo left Las Palmas for AEK Athens in a loan deal on Thursday.
(Reporting by Martyn Herman, editing by Ed Osmond)
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