His arrival from Lens was controversial with Chelsea found guilty in 2009 of having induced the player to break his contract.
Initially the Blues were barred from making signings until September 2011, although the Court of Arbitration for Sport overturned the ban earlier in 2010 - however Chelsea were required to pay £113,000 compensation to cover the player's development at the French club.
Kakuta has played in five out of six Champions League group games, starting in two, including the home game against group runners-up Marseille.
"It is a dream when you are young to play in the Champions League and I hope I will play more games," he added.
"It is always good to play with players with more experience, you learn quicker and to improve quicker is good for our development."
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