The Rangers are sending outfielder Lewis Brinson, right-hander Luis Ortiz and a player to be named later to the Brewers. Texas completed the deal a day after Lucroy blocked a preliminary agreement the Brewers had to send him to Cleveland.
This is the second year in a row at the deadline that the Rangers acquired a top player who had first rejected a deal to another team. They got All-Star left-hander Cole Hamels last season after the pitcher voided a proposed trade that would have sent him from Philadelphia to Houston.
Lucroy acknowledged the trade in a tweet on Monday.
Jeffress, a 28-year-old right-hander, is 2-2 with a 2.22 ERA in 47 appearances this season.
Ortiz, 20, is 4-6 with a 3.48 ERA for two clubs in the Rangers' minor league system. He's now pitching at Double-A Frisco. He was the Rangers' first-round pick (30th overall) in the 2014 draft.
Brinson, 22, an outfielder, is hitting .237 with 11 home runs and 41 RBIs in the minor leagues. He also was playing for Frisco at the time of the trade. He was the Giants' first-round pick (29th overall) in the 2012 draft.
Lucroy, 30, is batting .299 with 13 homers and 50 RBIs. He has a $4 million salary this year as part of a contract that includes a $5.25 million team option for 2017.
He thanked Milwaukee's fans.
The Rangers and the Brewers had been talking last week about a deal including Lucroy, but the talks ended when Milwaukee agreed to send Lucroy to Cleveland for four players. On Sunday morning, Lucroy refused to waive the no-trade provision in his contract and vetoed the trade to the Indians. Cleveland was one of eight teams he could block. He can't block a deal to the Rangers.
The Rangers sent young power-hitter Joey Gallo to Triple-A Round Rock on Monday after Monday's moves.