The forward will receive a three-year, $34 million deal, the sources said.
"The decision came down to whether KG wanted to keep playing," a source told the Boston Herald. "And once he decided that he did, it was going to be Boston. He wasn't going to leave Doc (Rivers) and those guys and play anywhere else."
The 36-year old Garnett just completed his fifth season in Boston after 12 years in Minnesota. He averaged 15.8 points and 8.2 rebounds per game during the regular season, but upped his averages to 19.2 and 10.3 in the playoffs.
The Celtics have one other big name heading into free agency in shooting guard Ray Allen. While he has also expressed a desire to return to Boston, sources told ESPN.com's Brian Windhorst that the NBA champion Miami Heat have made Allen their primary offseason target.
While the timing of Garnett's deal helps the Celtics sort out their free agent plans, the reported average annual value of the deal gives Boston more salary cap room to work with. Garnett made $21 million last season, but both parties needed to account for Garnett's higher age and lower expectations, while allowing for Garnett's importance to the team's immediate future.
Boston can use the remaining cap space to retain their key free agents or lure players outside the organization. However, if the Celtics choose to avoid paying the luxury tax, they will be allowed to use the full midlevel exception, which has been set at $5 million for the 2012-13 season.
That exception could be used for someone like Memphis Grizzlies guard O.J. Mayo. The Celtics reportedly nearly dealt Allen at the trade deadline for Mayo and Memphis did not extend Mayo a qualifying offer, making him an unrestricted free agent.
Garnett is in position to reach some notable NBA milestones. If he comes close to scoring 1,000 points during the 2012-13 season, he'll move into the top 15 on the NBA's all-time scoring list, surpassing the likes of Allen Iverson, Patrick Ewing and Jerry West. Similarly, if he grabs 500 rebounds next season, Garnett will vault into the top 10 in total rebounds in NBA history, moving past Hakeem Olajuwon and Wes Unseld.
Information from ESPNBoston.com's Celtics contributor Greg Payne contributed to this report.