Serving in the same capacity for Syracuse last year, Gale mentored the 26-year-old Estrada through his first full Triple-A season.
Milwaukee claimed Estrada in early February, while simultaneously clearing a 40-man roster spot by designating righthander Tim Dillard for assignment.
Dillard cleared waivers and was assigned to Triple-A Nashville.
Gale liked what he saw from Estrada, who started in 25 of his 27 appearances and went 9-5, 3.63 for the Chiefs. He struck out 98 batters in 136 innings and handed out a mere 2.2 walks per nine innings.
But that pitcher has yet to make the jump to the big leagues. In two late-season callups to Washington in the past two seasons, Estrada compiled a 7.20 ERA working mostly as a reliever.
"You take players based on their upside, not what they have done thus far in the majors," assistant general manager Gord Ash said. "Rich Gale liked him and made a strong recommendation to (pro scouting director) Dick Groch.
"We went on that, plus our own thorough scouting reports."
The 6-foot, 180-pound Estrada is considered a bit undersized for a righthanded starter, but he's a strike-thrower with a fastball in the low 90s and outstanding changeup. He also throws a sharp curveball in the 78-81 mph range.
Estrada, a sixth-round pick in 2005 from Long Beach State, has two minor league options remaining but had been designated for assignment by the Nationals to make room for free agent reliever Tyler Walker.
The Brewers considered Estrada an upgrade over Dillard, who spent most of 2009 at Nashville after converting from relieving to starting.
"In making our decision, we just felt Estrada might have a better chance of helping us than Dillard," Ash said. "(Dillard) just hasn't gotten over the hump to this point."
Estrada became the fourth player claimed on waivers by the Brewers this offseason, joining catcher George Kottaras (Red Sox), shortstop Luis Cruz (Pirates) and second baseman/outfielder Joe Inglett (Rangers).
• Righthander Chris Smith accepted an outright assignment to Nashville after being designated for assignment to clear a spot for Inglett. The 28-year-old, who had the right to become a free agent, pitched in 35 games for the Brewers last season.
• Former Brewers minor league catcher Nestor Corredor was helping run the team's new baseball academy in the Dominican Republic.