Garnett, who was an unrestricted free agent, will sign a two-year deal, according to ESPN.com's Marc Stein. No deal can be officially signed until Thursday.
"I'm incredibly excited and rejuvenated to be a part of this talented, committed team," Garnett said, according to KSTP.
Garnett, 39, spent his first 12 seasons in Minnesota before being traded to the Boston Celtics before the 2007-08 season. He won an NBA championship in his first season with the team.
He was traded to the Brooklyn Nets during the 2013 off-season and spent the next year and a half there before he was dealt back to Minnesota in February.
After the season, Timberwolves head coach Flip Saunders said he thought that Garnett would return for the 2015-16 season.
Garnett averaged 6.9 points and 6.6 rebounds in 47 games this season, playing in only five games after being traded back to Minnesota.
Garnett, a 15-time NBA All-Star and four-time All-NBA First Team selection, has career averages of 18.2 points, 10.2 rebounds and 1.4 blocks. He is the NBA's active leader in games played.
The Timberwolves finished the season 16-66, the NBA’s worst record. The team selected former Kentucky center Karl-Anthony Towns with the first overall pick in last month’s NBA draft and later picked former Duke guard Tyus Jones with the 24th pick.
The team announced Tuesday that both Towns and Jones had signed their rookie contracts.
- Scooby Axson