Sources told ESPN.com that the long-anticipated deal is on course to be finalized later Friday.
ESPN.com reported in July that the Bucks and Hensonhad entered into advanced negotiations on an extension, but the deal took nearly three more months to complete.
"We're close," Henson told reporters at Bucks camp earlier this week. "We're just trying to work out some details. It's a process; we'll see what happens. But I definitely want to be here for a long time."
The deal that has since been struck will secure Henson as part of a growing and blossoming core in Milwaukee that includes guards Jabari Parker and Michael Carter-Williams, versatile forward Giannis Antetokounmpo, newly signed center Greg Monroe and re-signed forward Khris Middleton.
Henson is widely regarded as one of the league's underrated frontcourt defenders. He averaged a seemingly modest 7.0 points and 4.7 rebounds in 18.3 minutes per game for the Bucks last season, but also averaged 2.0 blocks per game to rank sixth in the league in that category despite the limited playing time.
The 24-year-old -- who has been pursued via trade by several interested teams in recent years -- also posted a PER well above the league average (18.1) and saw his playing time increase to 25.5 minutes per game in the playoffs.
The Bucks finished 41-41 last season first-year coach Jason Kidd despite their youth and have now cemented a strong six-player core under Kidd with the addition of Monroe and the long-term deals reached over the past few months with Henson and Middleton.