Hayward initially revealed the news in an article for the Players' Tribune on July 4.
According to ESPN.com's Chris Forsberg, Hayward agreed to a max contract of four years and $128 million.
The finalization of the deal was delayed by Boston's need to clear enough salary cap space to make it happen.
Boston renounced the rights of multiple players, including center Kelly Olynyk, before trading guard Avery Bradley to the Detroit Pistons for forward Marcus Morris.
The movement was enough to make room for Hayward, who will reunited with his college head coach at Butler, Brad Stevens.
Boston finished first in the Eastern Conference during the 2016-17 regular season, and it has added an All-Star to the mix who has gotten better with each passing year.
The 27-year-old enjoyed a career year last season with 21.9 points, 5.4 rebounds and 3.5 assists per game. He also helped the Utah Jazz advance to the second round of the playoffs.
Hayward will join a deep and talented roster in Boston that already includes dynamic offensive guard Isaiah Thomas, All-Star big man Al Horford and rookie No. 3 overall draft pick Jayson Tatum.