Eto'o and Cole, both 33, had been expected to leave the Premier League side after their contracts came to an end last month.
Cole spent eight seasons at Chelsea after joining from Arsenal. He made 338 appearances and helped them to Champions League glory in 2012, the Premier League and FA Cup double in 2010 and a Europa League triumph in 2013.
He retired from the England side after missing out on a place in Roy Hodgson's 23-man squad for the World Cup in Brazil.
"Cole has a very strong claim to be this club's greatest player in his position of all time," Chelsea said in a statement.
"Chelsea Football Club thanks Ashley for the fantastic service he gave throughout his eight years here and for helping to bring so many trophies home. We wish him well for the future."
Cole's long-time club and international team mate Frank Lampard also left Stamford Bridge last month.
Eto'o arrived from Russian team Anzhi Makhachkala, scoring nine goals in 21 league appearances in his one season at Stamford Bridge.
Schwarzer, 41, made 13 appearances for the club last season after joining on a free transfer from Fulham.
In December he became the oldest player to make his debut in the Champions League when he featured against Steaua Bucharest.
Schwarzer will again provide cover for Czech Petr Cech and potentially young Belgium international Thibaut Courtois who could return to the club after spending three seasons with Atletico Madrid.
(Reporting by Josh Reich, editing by Tony Jimenez)
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