The teams both announced the trade Monday, two days after reportedly agreeing to the deal.
"We're excited to add Michael to our roster," Bulls general manager Gar Forman said in a statement. "He is a two-way player who adds versatility and depth to our backcourt rotation."
A source close to Carter-Williams told ESPN's Jeff Goodman that the guard was informed he was being traded to Chicago late Saturday night.
Sources said the Bucks, who have been openly looking for more shooting and defense on the perimeter in the wake of a long-term injury suffered by starter Khris Middleton just days before training camp, targeted Snell to give them some much-needed help on the wing.
The Bucks and Bulls met Saturday night in Chicago in a preseason game, but neither Carter-Williams nor Snell played.
ESPN reported earlier this month that the Bucks had unsuccessfully offered Carter-Williams -- who won NBA Rookie of the Year honors in Philadelphia in 2013-14 -- to Sacramento in a proposed deal for Kings guard Ben McLemore.
But the Bucks, sources say, are intrigued by Snell's potential -- both as a fill-in for Middleton and as a potential backup -- after he shot 35 percent from long distance last season. Should the deal be consummated, Milwaukee is expected to open contract extension talks with Snell, sources told ESPN's Brian Windhorst.
For the Bulls, adding Carter-Williams would provide them with a proven second point guard alongside Rajon Rondo, who signed a two-year deal in the offseason in which only $3 million of his $13.4 million salary in 2017-18 is guaranteed.
The Bucks surrendered Brandon Knight in a three-team trade with Philadelphia and Phoenix to acquire Carter-Williams in February 2015, but the move never panned out as Milwaukee had hoped, with Carter-Williams' shooting struggles and the emergence of star Giannis Antetokounmpo landing him on the bench.
Both Carter-Williams and Snell are 2013 first-round picks eligible for extensions ahead of the Oct. 31 deadline, although neither seemed likely to land an extension before these trade talks.
Carter-Williams lost his starting spot in Milwaukee this past winter before undergoing hip surgery. Snell had likewise fallen out of favor in Chicago and would have struggled for playing time on the wing with the Bulls behind Dwyane Wade, Jimmy Butler and Doug McDermott.