The agreement, which the team hasn't announced, would be one of the largest in Phillies history.
The deal does not include a no-trade clause, Jon Heyman of MLB Network reports.
The Chicago White Sox also made an offer to Wheeler, and it was for more than $118 million, reports The Athletic's Ken Rosenthal. The pitcher's wife is from New Jersey, which could have played an important role in his final decision, Rosenthal adds.
Wheeler was one of the top pitchers available in free agency this offseason.
The 29-year-old owns a career 44-38 record with a 3.77 ERA and 1.29 WHIP in 126 starts, all coming with the New York Mets.
Even though Wheeler missed the 2015 and 2016 campaigns while recovering from Tommy John surgery and a flexor strain in his pitching arm, his last two seasons have been solid, helping him to earn a significant payday.
Wheeler's 2018-19 stats
The hurler will join a Phillies rotation that ranked 17th in major-league ERA last season and near the bottom in combined WAR, according to FanGraphs.
2020 projected rotation (2019 stats)
Because Wheeler was extended a qualifying offer, the Mets will receive a compensation pick after competitive balance round B in the 2020 draft. The Phillies will forfeit their second-round pick and $500,000 from their international bonus pool, according to MLB Pipeline.
Before his reported agreement with the Phillies, Wheeler also drew interest from the White Sox, Minnesota Twins, Cincinnati Reds, Texas Rangers, Los Angeles Angels, and Toronto Blue Jays.