Kakuta, 23, moved to Stamford Bridge from Lens in 2007 and was on loan at Rayo Vallecano last season, where he played 35 games.
The Frenchman played 16 times for the Blues, but spent time on loan at six different clubs.
In September 2009, Chelsea were barred from signing new players after being found guilty of inducing Kakuta to break his contract with Lens.
The ban was lifted by a court in February 2010 after the two clubs reached an agreement on his signing.
It is thought Sevilla have had to pay a fee for Kakuta because he is under 24.
In October 2014, failed footballer Medi Abalimba was sentenced to four years in prison after masquerading as Kakuta.
Manchester Crown Court heard Abalimba went on a £20,000 shopping spree at Selfridges, stayed at top hotels and even hired a helicopter.
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Chelsea's out-of-contract winger Gael Kakuta has joined La Liga side Sevilla.