Estrada, 26, made 15 appearances during brief stints in the Majors with Washington in 2008 and 2009, but spent most of last season at Triple-A Syracuse, where he was 9-5 with a 3.63 ERA in 25 starts and two relief appearances. His pitching coach at the end of the season was Rich Gale, who was hired by the Brewers in October to serve the same role beginning next season at Triple-A Nashville.
"Based on Rich's recommendation, we decided to make a claim," Brewers assistant general manager Gord Ash said. "He's not exactly young at 26, but he's a younger guy that we had some strong reports on."
Estrada has two Minor League options remaining.
Dillard, also 26, appeared briefly for the Brewers in both 2008 and 2009, but walked 11 versus six strikeouts in 18 2/3 innings. He has struggled to translate his raw "stuff" -- including a heavy, sinking fastball -- into sustained big league success.
"That may be because we've switched roles on him. He's started, he's relieved, we've even thought about him closing out games, which didn't seem to work out," Ash said. "There are players that just don't make that transition as easily as others, and he has not made it.
"Hopefully, we can work out a way to keep Dillard. If we lose him, it's like making a trade [for Estrada], I guess."
Dillard was 11-7 with a 4.51 ERA in 24 starts at Nashville last season. He was the Brewers' 34th-round Draft pick in 2002.
Estrada will wear uniform No. 74 from the Brewers.
Adam McCalvy is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.