The Bucks also receive forward Ekpe Udoh and centre Kwame Brown in the deal first reported by the Milwaukee Journal Sentinel on its website.
The trade represents a parting of ways between the Bucks and Bogut, the No. 1 overall pick in the 2005 draft who has struggled with injuries. It also allows the Bucks to rid themselves of Jackson, who had fallen out of favour with coach Scott Skiles and now gets to rejoin his former team.
For the Warriors, the trade breaks up the small backcourt of Ellis and Stephen Curry and brings in the type of big man the franchise has been seeking for years.
"We're extremely excited to acquire a player the calibre of Andrew Bogut, who we think is certainly one of the top centres in the NBA," general manager Larry Riley said. "He will add an element of toughness to our team and will provide us with scoring, rebounding and a defensive presence in the middle. We've lacked those elements in recent years and think that Andrew's addition will be a key factor in the growth of our team."
Ellis and Udoh left the team before Golden State's 115-89 win at Sacramento. The deal was announced shortly after the game ended. Ellis, whose future has been subject of trade speculation, was reminded that he recently said he wanted to stay with the Warriors long term.
"Well, everybody says that," Ellis said. "But sometimes it (doesn't) always work out like that."
The players won't be separated from their respective former teams for very long, as the Warriors host the Bucks on Friday night.
Bogut fractured his left ankle Jan. 25 against Houston when he landed awkwardly, and it's not clear if he'll be able to return this season. The original timetable for his recovery was eight to 12 weeks. It's one of several significant injuries that have plagued Bogut throughout his career.
Bogut missed the end of the 2009-10 season when he dislocated his right elbow, sprained his right wrist and broke his right hand in a hard fall to the floor. The injury bothered him for much of last season.
Bogut also missed significant time with an injured lower back in the 2008-09 season.
When Bogut has played, he has played well. In 408 career games, he is averaging 12.7 points, 9.3 rebounds and 1.6 blocked shots.
The Bucks struggled in February without Bogut, but have won four of their last five to chase down the struggling New York Knicks in a race for what would be the No. 8 playoff seed in the Eastern Conference.
Jackson, meanwhile, hasn't played since Feb. 19, recently sitting out with what the team has described as a hamstring injury. Skiles benched him for a game in January after he missed a shootaround, he was suspended one game by the NBA for verbally abusing an official and his playing time has been limited ever since.
The deal brings the enigmatic "Captain Jack" back to the Bay Area. He helped lead the team's only playoff run since 1994, a surprising trip to the second round in 2007. In October 2009, the disgruntled Golden State star asked to relinquish his captain title during a meeting with Riley and then-Warriors coach Don Nelson. He was traded to Charlotte the next month.
Ellis has been the Warriors' main offensive threat, averaging 21.9 points. But Golden State struggled to win with the backcourt tandem of Ellis and Curry. The deal clears a spot for 6-foot-7 rookie Klay Thompson to take over at shooting guard, adding needed size to the starting backcourt
Ellis signed a six-year, $66 million contract in July 2008, then injured his left ankle in August in a low-speed moped crash — an off-season activity prohibited in his deal as is a standard provision for contracts around the league. It cost him a 30-game suspension without pay.
Udoh is averaging 5.5 points and 3.9 rebounds in 21.8 minutes for the Warriors. Udoh is an athletic power forward who was Golden State's sixth pick in the 2010 draft out of Baylor. The Warriors hoped he would become a reliable defender, rebounder and shot blocker.
Brown, a former No. 1 overall pick by Washington, is likely out for the season with a chest injury and will be eligible to be a free agent this summer.
"The difficult part of this transaction is having to part ways with several players who we really value and one, in particular, Monta Ellis, who has been instrumental in our organization for the last several years," Riley said. "We wish Monta, Ekpe and Kwame the best of luck in Milwaukee and thank them for their many contributions."
AP Sports Writer Janie McCauley and Josh Dubow contributed to this report.