Garnett and the Timberwolves agreed in principle to a two-year deal, sources confirmed to ESPN's Marc Stein. Garnett will sign the deal when the NBA's moratorium on new contracts is lifted later this week.
"I'm incredibly excited and rejuvenated to be part of this talented, committed team," Garnett told KSTP Sports, which reported the deal earlier Tuesday.
Minnesota is expecting the 39-year-old Garnett to play in the 20-minute range next season, sources told Stein. The 2004 league MVP would play past his 40th birthday if he sees out both years of the contract.
The Timberwolves also announced the signing of Towns, the top overall draft pick, and fellow rookie Tyus Jones, the No. 24 pick.
Towns' three-year contract is worth just over $14.9 million, according to RealGM.com, and it includes a fourth-year option.
Garnett was reunited with the Timberwolves last season in a trade with the Brooklyn Nets. Garnett spent his first 12 seasons in Minnesota before being traded to the Boston Celtics prior to the 2007-08 season.
The rebuilding Timberwolves hope that Towns and last year's No. 1 pick, Andrew Wiggins, can be a formidable duo for years to come. Minnesota acquired Wiggins in the blockbuster trade that sent Kevin Love to Cleveland last summer.
ESPN.com's Marc Stein contributed to this report.