Ian Begley of ESPN.com first reported the news Wednesday.
The decision represents a change of heart for Stoudemire, who announced his retirement from basketball in September after helping Hapoel Jerusalem, an Israeli team for which he serves as a shareholder, win the Israeli Basketball Premier League championship last season.
He spent 14 years in the NBA, including stops with the Phoenix Suns, New York Knicks, Dallas Mavericks and Miami Heat.
The 35-year-old Florida native averaged 18.9 points, 7.8 rebounds and 1.2 blocks across 846 career regular-season games. His consistent success allowed him to earn six All-Star selections and a first-team All-NBA nod for the 2006-07 campaign.
Stoudemire's arrival should help Tri-State, which added Robinson to the O'Neal-led roster last month, bolster its chances of title contention after going 3-5 during the league's debut season in 2017.