The Timberwolves announced the signing on Wednesday after first agreeing to terms with him on a deal worth $8 million last week.
The 28-year-old Hill averaged 8.8 points and 6.2 rebounds in 73 games for the Indiana Pacers last season. The 6-foot-10 Hill has also played for the Lakers, Rockets and Knicks in his career.
Hill's addition beefs up the frontcourt depth behind starters Karl-Anthony Towns and Gorgui Dieng. The Timberwolves struggled in that area last season after Kevin Garnett and Nikola Pekovic were sidelined by injuries, requiring Towns and Dieng to play heavy minutes over the last two months.
It remains unclear if Garnett will return for a 22nd season.