The Colombia international completed his widely-tipped move to the Premier League champions from Ligue 1 side Monaco on Friday afternoon.
The 29-year-old endured a miserable season at Old Trafford after he scored just four goals in 29 games during his long-stay loan at Manchester United.
Former Liverpool midfielder Redknapp doesn’t expect the South American striker to be much more successful at the west London side.
“He’s going to find himself on the bench an awful lot next year,” Redknapp told Sky Sports News.
“I watched Radamel Falcao in his Atletico Madrid days and he was one of the best centre forwards I think I’ve ever seen.
“Now he’s gone to Chelsea and probably what Chelsea need is a striker that’s going to be happy not to play, and maybe have to fill in at times when there is an injury, because you look at the players he’s going to be contending with like Diego Costa, who is going to be first choice.”
Falcao will linked up with his former Atletico Madrid team-mates Thibaut Courtois and Filipe Luis at Stamford Bridge.
The South American 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.
Falcao scored 52 times in 68 La Liga games before his move to Monaco in 2013.
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