The 23-year-old has agreed personal terms with Andre Villas-Boas' side and passed a medical, after a transfer fee was confirmed on Sunday.
Chadli scored twice in Twente's win over Tottenham in the UEFA Champions League two seasons ago and will join the club's pre-season trip to Monaco on Saturday.
A statement on the club's website read: "We are delighted to confirm the signing of Nacer Chadli from FC Twente after the player agreed personal terms and successfully completed his medical.
"The Belgium international is expected to be available for the first time when we travel to Monaco for our pre-season fixture on Saturday, August 3."
Chadli, who was also a reported target for Swansea and Fulham, was an important part of Twente's side last season, making 26 Eredivisie appearances and scoring 12 goals as Michel Jansen's side finished sixth.
The Enschede club missed out on a spot in the UEFA Europa League, however, after a losing a play-off to Utrecht.
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