Adrian Wojnarowski of ESPN first reported word of the star's decision to turn down the $30.1 million option.
The 33-year-old Dominican Republic native remained productive for the Celtics this past season as the team attempted to juggle an overcrowded rotation. He averaged 13.6 points, 6.7 rebounds, 4.2 assists and 1.3 blocks across 68 appearances.
Horford, who has earned one All-Star selection in three years with Boston, ranked fifth among centers in ESPN's real plus-minus for 2018-19.
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The two-time NCAA champion at Florida, who the Atlanta Hawks selected with the third overall pick in the 2007 NBA draft, told Brian Robb of the Boston Sports Journal in March he has plenty of time left in the league:
"For me, as long as I'm healthy and feel good, I would like to play until I'm 40. Why not? As long as I'm healthy and feel good. I don't want to be out there struggling or hurt or things like that. I really take the time to work on my body and I enjoy the game, so I wouldn't see why I wouldn't keep playing on it. I'm not going to put a limit on it. I'm just going to keep playing as long as I feel good."
Horford's all-around game, which has evolved in recent years to include three-point shooting, could make that possible.
Although turning down over $30 million guaranteed for next season comes with risk, Horford should be able to secure a long-term pact that gives him more financial stability.
He could still return to Boston on a new deal, but he may want to see what type of alternatives are available on the open market before he decides.