The former England international touched down in Istanbul on Friday for a medical with Kasimpasa and to sign terms.
However, club owner Turgay Ciner sent his private jet to collect Drinwater and take him to Istanbul on Friday.
England international Drinkwater has managed only a handful of appearances so far this season. He's played once for Chelsea reserves in the EFL Trophy and three times for their Premier League 2 team, which included seeing him sent off.
With his loan running to the end of this season, Drinkwater will remain contracted to Chelsea for another year. His deal doesn't expire until 2022.
- updated January 18