The 29-year-old was a free agent after his contract at Anfield expired in the summer.
“We have signed a three-year contract with free agent Daniel Sturridge, with a one-year option,” read a statement on the Super Lig club’s website.
Sturridge made 29 appearances for Liverpool last season, mostly as a substitute, with the last of those coming late on in the 4-0 Anfield win over Barcelona in the second leg of the Champions League semi-final.
The 26-cap England international, who was an unused substitute in the Reds’ final victory over Tottenham in Madrid, scored the first goal of Liverpool’s Champions League campaign last season against Paris St Germain in a run of four goals in his first seven matches.
However, he was never able to displace Roberto Firmino as first-choice striker and therefore was never likely to earn a contract extension.
Sturridge, who in July was banned from football for two weeks and fined £75,000 after breaching betting rules, had been training on his own in the United States prior to signing a deal with Trabzonspor.