Sources had told ESPN FC that Sturridge arrived in Turkey on Tuesday where he underwent the formalities before finalising the move.
The 29-year-old was a free agent after being released by Liverpool in the summer and was courted by Fenerbahce, while clubs in La Liga, MLS and Qatar had been interested in signing him.
However, he has agreed to join Trabzonspor in deal understood to be worth just short of £3 million per year.
Sturridge began his career at Manchester City before joining Chelsea on a free transfer in 2009, where he stayed until January 2013 before joining Liverpool.
The England striker has two Champions League medals from his time with Chelsea and Liverpool as well as a Premier League title while at Stamford Bridge.
Information from ESPN FC correspondent Melissa Reddy was used in this report