A news conference will be held early this week announcing the deal. Rambis' agent, Lon Rosen, was not available for comment.
Rambis, who made a name for himself with his rugged play during the Showtime era of the 1980s, spent the last 10 seasons as an assistant to Phil Jackson.
The Lakers will have to decide whether they'll fill the vacant spot, which leaves Jackson with three assistants: Frank Hamblen, Brian Shaw and Jim Cleamons. Rambis ran the team's defense, which limited the Orlando Magic to an average of 91.2 points a game in the NBA Finals, which the Lakers won for the 15th time.
Rambis takes over a young Timberwolves team that finished 24-58 last season and fired Kevin McHale in June, succeeding the person who clotheslined him during the 1984 Finals. McHale was a star forward for the Boston Celtics, who defeated the Lakers in seven games in that series. Rambis won four championships in his nine-year playing career with the Lakers.
The coaching announcement caps off a busy summer for Rambis, who was chosen for the Minnesota job over TV analyst and former star point guard Mark Jackson and Houston Rockets assistant Elston Turner. The Sacramento Kings offered Rambis their head coaching position but ultimately chose Paul Westphal after Rambis asked for more than the two-year contract and money that was offered. He was also interviewed for the head coaching vacancy with the Philadelphia 76ers.
Rambis has head coaching experience, in a limited fashion. He was 25-13 in 1999 with the Lakers after taking over as interim coach for the fired Del Harris.
Jackson was soon hired by the Lakers, and eventually Rambis joined the staff as an assistant. He has also filled in at certain times because of medical issues involving Jackson, who briefly floated the idea Rambis could assume coaching duties on various trips in the 2009-10 season.
Times staff writer Mike Bresnahan contributed to this report.