The deal includes an option to extend his stay by a further 12 months.
Terms of the contract were not revealed, but it's understood the multi-year deal is worth £3 million per season, according to Melissa Reddy of ESPN FC.
Along with D.C. United, up to 13 teams from the around the globe were courting Sturridge, according to Chris Bascombe of The Telegraph. However, he ultimately decided to join a Trabzonspor side that finished six points back of Super Lig winners Galatasaray last season.
Sturridge was an unused substitute on the Liverpool team that claimed the Champions League title in June. He also won the coveted trophy at Chelsea in 2012.
The 31-year-old ended his six-year stay at Liverpool with 67 goals in 160 appearances.