Cousins, 31, will sign a non-guaranteed deal to join the defending NBA champions, sources said. Teams must guarantee contracts for the balance of the season by Jan. 7.
The Bucks have been without center Brook Lopez because of a back injury and needed some more size to bolster their front line.
The Bucks haven't officially announced the move, but following their 118-100 win against the Indiana Pacers on Sunday, both star Giannis Antetokounmpo and coach Mike Budenholzer spoke of the team's need to have another big with Lopez sidelined.
"Obviously, Brook is a big part of what we do, can't wait for him to get back healthy, but at the end of the day, without Brook, we don't have another big," Antetokounmpo said. "I feel like it's a lot of load on me and Bobby [Portis] to be those bigs all the time on the court, so just adding another guy, that'll be nice."
Added Budenholzer: "We're playing Giannis and Bobby really as our two bigs right now, so I think when you look at the depth chart and look at how we're subbing and everything, depth at the big position is something that we could use."
Cousins has averaged 20.4 points and 10.6 rebounds in his 10-year NBA career, which includes two significant lower-leg injuries in recent years -- a torn ACL and an Achilles tear. He is a four-time All-Star and a two-time All-NBA second-team selection (2015 and 2016).
He played seven years with the Sacramento Kings until a trade to New Orleans in 2017, and signed successive free-agent deals with Golden State, Houston, the Clippers and now the Bucks.
ESPN's Jamal Collier contributed to this report.