The Colombia striker will return to the Premier League on another season-long switch from Monaco after spending an unhappy 2014-15 campaign at Manchester United.
Chelsea have agreed terms with Monaco over the season-long loan of striker Radamel Falcao.
The Colombia international, who was a £50 million signing for the Ligue 1 side in 2013, will spend the duration of the 2015-16 campaign at Stamford Bridge.
Chelsea youngster Mario Pasalic, a 20-year-old Croatian midfielder who spent last season at Elche, will join Monaco on loan as part of the deal.
"I am very happy to be joining Chelsea and can't wait to start training and help with our aim of retaining the league title and being successful in Europe," Falcao told the club's official website.
The 29-year-old scored nine goals in 17 games in his first season with Monaco but had his campaign ended by a serious knee injury and missed last summer's World Cup.
Falcao then joined United on loan on deadline day last year but struggled to make an impact at Old Trafford, scoring only four times in 29 games.
Prior to his move to Monaco he was recognised as one of the world's leading strikers, scoring 70 goals in two seasons at Atletico Madrid and netting a hat-trick in the 2012 Super Cup against Chelsea.
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