The 29-year-old striker trained with Juan Cuadrado and Willian in New York after he linked up with the Premier League champions following an extended break after the Copa America.
Falcao moved to the west London side on a season-long loan from Ligue 1 side Monaco earlier this summer after Manchester United opted not to make his deal permanent at Old Trafford.
And the Chelsea forward’s wife uploaded a post on her Instagram page following the former Atletico Madrid man’s first training session with Jose Mourinho’s squad.
Toran wrote: “I’m happy for this new chapter at this marvellous club. God is good”
Falcao endured a miserable season at Old Trafford after he scored just four goals in 29 games during his long-stay loan at United.
Falcao scored 52 times in 68 La Liga games before his move to Monaco in 2013.
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