A source told ESPN the fourth year of Pierce's contract -- the main point of contention in the negotiations -- is fully guaranteed.
It was not immediately known if the contract contains a no-trade clause, which Pierce is eligible for by virtue of having at least eight years of service time and four with the same team.
Pierce opted out of the final year of his contract and sacrificed $21.5 million to give the Celtics room to re-sign Ray Allen and add another piece to a Boston team that came within one win of its second NBA title in three years.
Multiple media outlets reported Friday that the sides had reached an agreement on a four-year deal between $60 and $62 million.
Celtics spokesman Jeff Twiss had no comment when reached Friday by The Associated Press.
Pierce has spent his entire 12-year career with the Celtics. He is second only to Larry Bird among longtime Celtics in points per game. Pierce is first in 3-pointers, second in steals, third in total points, eighth in games played and ninth in rebounds.
ESPN The Magazine's Ric Bucher, ESPN.com's Marc Stein and The Associated Press contributed to this report.