The contract, which includes a fifth-year vesting option for 2018, could be worth up to $67 million based on performance bonuses.
Garza gets $12.5 million a season, with $2 million annually deferred without interest. The deferred money is payable in four installments each Dec. 15 starting in 2018. He can earn an additional $1 million annually in performance bonuses: $500,000 each for 30 starts and 190 innings.
The deal includes a $13 million option for 2018 that would become guaranteed if he makes 110 starts during the next four years, pitches 155 innings in 2017 and is not on the disabled list at the end of that season. Milwaukee also would get an extra year at a relatively low salary if he has a significant arm injury.
The Brewers, who are looking to rebound from a disappointing 74-88 season in 2013, also announced the deal on their official Twitter account.
— Milwaukee Brewers (@Brewers) January 26, 2014
Earlier Sunday afternoon, Brewers owner Mark Attanasio was on stage during a question-and-answer session at a fan event and said a deal was in place.
General manager Doug Melvin called Garza an "established, top-of-the-rotation pitcher."
"The thing about signing Matt now, it gives us a lot more depth and, as you know, during a baseball season, you never use five starters," Melvin said. "So, just kind of wait and see how spring training unfolds, and always having the available depth is important to stay in a 162-game season."
The 30-year-old Garza went 10-6 with a 3.82 ERA last season for the Chicago Cubs and Texas Rangers. The right-hander missed most of the first two months while recovering from an injury that affected his side and back.
Garza was looking forward to pitching -- and hitting -- back in the NL Central.
"It's fun. I like the Central, I like pitching in the Central," Garza said in a conference call. "I like swinging the bat in the big parks."
"We've said now for a couple of years that we're focusing on pitching and pitching depth," Attanasio told reporters. "You can never have enough pitching depth, and I would argue we have as much pitching depth as we've had [in] my 10 seasons of ownership."
Garza was the MVP of the 2008 AL Championship Series, beating Boston twice while with Tampa Bay. He also has thrown the only no-hitter in Rays' history, on July 26, 2010, against Detroit.
His signing had been rumored for days, though the Brewers were seemingly a surprise suitor for Garza's services. The team issued a statement Thursday that they were in talks with Garza but hadn't reached a deal then.
"These deals can go to the 11th hour and then not come together," Attanasio said. "So you don't know until you know."
Information from The Associated Press was used in this report.