The 31-year-old Lind hit .321 with six homers and 40 RBIs in 96 games last season, when he missed extensive time with a back injury and then a hurt right foot. He has a .273 career average with 146 homers and 519 RBIs.
Just before the trade, the Blue Jays exercised his $7.5 million option, preventing Lind from becoming a free agent.
"He's a good fit for us now. We didn't want to wait through the free-agent season," Brewers general manager Doug Melvin said during a telephone interview. "We think our ballpark is a good fit for him. ... Positional-wise, this was just a real big need -- it's been that since Prince (Fielder) left."
Milwaukee expects Lind to be the primary starter at first base and play perhaps 140 games.
"Getting him off the turf (will help)," Melvin said.
Estrada, also 31, was 7-6 with a 4.36 ERA in 18 starts and 21 relief appearances, when he made $3,365,500. He is 23-26 with a 4.23 in seven seasons with Washington and Milwaukee.
Estrada is eligible for salary arbitration and can become a free agent after the 2015 World Series.
Milwaukee concluded that as a flyball pitcher, Estrada may not have been ideally suited for Miller Park.
"We thought it was good baseball trade from that standpoint," Melvin said.
Edwin Encarnacion figures to be the Blue Jays' regular first baseman, freeing up the club to rotate players at designated hitter. Justin Smoak, claimed off waivers from Seattle this week, may provide depth in both areas.
"There's no question the offense and the bat will be missed, but we have some other areas of need on the club and sometimes you have to make a tough choice and a tough decision," Blue Jays GM Alex Anthopoulos said of Lind during a conference call.
The Blue Jays declined options on right-handers Dustin McGowan, Brandon Morrow and Sergio Santos, allowing them to become eligible for free agency. McGowan gets a $500,000 buyout rather than a $4 million salary, Morrow receives a $1 million buyout rather than a $10 million salary, and Santos gets a $750,000 buyout instead of a $6 million salary.
Toronto also declined a $3.65 million option on Smoak, who gets a $150,000 buyout and becomes eligible for salary arbitration.
The Blue Jays extended a $15.3 million qualifying offer to free-agent outfielder Melky Cabrera, who has until Nov. 10 to accept. If Cabrera signs a major league contract with another club before the amateur draft in June, Toronto would receive a draft pick as compensation at the end of the first round.
NOTES: Melvin said OF Ryan Braun is doing well following a medical procedure to address a nerve problem near his right thumb. While Braun has swung a bat, "he hasn't swung off a 96-97 mph fastball," Melvin said.