The deal could rise to as much as $48 million over the four years if Henson meets incentive clauses, league sources said.
The deal also includes a signing bonus and front-loaded payments, sources said.
The front-loading of money will minimize the financial impact of a potential work stoppage in 2017.
For Henson and his modest numbers thus far in the NBA, this is a tremendous deal. For the Bucks, it is a calculated hedge on the restricted free-agent market next summer – which could have included Henson – that could be a boon for big men.
Jim Tanner, Henson’s agent, and Bucks general manager John Hammond had been negotiating the deal throughout the summer and finalized the terms Friday, league sources said.
Henson’s ability to play without the ball, defend and block shots gives the Bucks an important element for a franchise that promises to become a major factor in the Eastern Conference.
Henson, 24, averaged seven points, 4.7 rebounds and two blocks for Milwaukee a season ago. In his three NBA seasons, Henson has averaged 8.1 points, 5.5 rebounds and 1.5 blocks.
Henson was the 14th overall pick in the 2012 NBA draft out of North Carolina.