The Colombia international joined the Blues on a season-long loan deal from Monaco earlier this summer as Jose Mourinho moved to bolster his attacking options at Stamford Bridge.
Falcao failed to live up to expectations at Old Trafford last season and only managed to score four goals in the Premier League for Louis van Gaal’s men.
But Costa was delighted to see the west London club wrap up a deal to sign the former Porto forward for the forthcoming season.
Costa is quoted as saying by Goal: “It’s good for us that he didn’t have the best of seasons as that’s why he’s now with us.
“We know that Falcao is a hugely talented player. The only thing he needs is to feel loved and trusted, and he will get both here.
“The manager is very happy to have brought him in and we are all very excited to have him in our squad because he’s a great player.
“He gets on very well with his team-mates and he will help us a lot off the field too.”
Falcao has linked up with his former Atletico Madrid team-mates Costa, Thibaut Courtois and Filipe Luis at Stamford Bridge.
The striker memorably scored a hat-trick against Chelsea in a 4-1 victory over the then-Champions League holders in the Uefa Super Cup in Monaco back in 2012.
Falcao scored 52 times in 68 La Liga games before his move to Monaco in 2013.
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