Caballero, 35, was available on a free transfer after being released by Manchester City and expressed his happiness at joining the Premier League champions, who are primed to ramp up their summer recruitment drive with the £36m signing of Bakayoko, the man expected to replace the Manchester United-bound Nemanja Matic.
Caballero featured prominently for Manchester City last season, making 26 appearances in all competitions as Pep Guardiola ended his first season in England without a trophy.
The former Malaga star joined Manchester City in the summer of 2014, but the arrival of Benfica goalkeeper Ederson Moraes at The Etihad Stadium all but ended Caballero's stint in the north-west.
"I am very happy to join Chelsea, the champions of England," Caballero told the club's official website. "I am looking forward to meeting the guys and helping the club achieve more success in the coming season."
Caballero will now provide competition for Chelsea's first-choice goalkeeper Thibaut Courtois after his previous understudy Asmir Begovic was sold to Bournemouth for £10m earlier this summer.
Chelsea also have another experienced goalkeeper in the form of Eduardo on their books, but the club's technical director Michael Emenalo believes there was a need for Antonio Conte's side to bring in a new stopper with a strong background in English football.
"We are very happy to have Willy on board," Emenalo said. "He knows the Premier League and is tried and tested at the top of the game. We have three experienced goalkeepers and we look forward to welcoming him to the club when the squad returns to pre-season training.'
Caballero is expected to be the first of a number of new players to arrive at Stamford Bridge this season. Along with Bakayoko, Chelsea are currently in talks with Juventus over defender Alex Sandro, who could command a fee of £60m, while they are also in discussions with Roma regarding German centre-back Antonio Rudiger. Romelu Lukaku remains a target but Everton's £100m valuation of the forward is a major stumbling block.