Right-handers Greg Aquino and Claudio Vargas also went to Milwaukee, while the Diamondbacks obtained a pair of youngsters, left-hander Dana Eveland and outfielder Dave Krynzel.
Davis, 31, is 62-63 with a 4.35 ERA in eight major league seasons. He was 11-11 with a 4.91 ERA in 34 starts last season with Milwaukee and, like Estrada, is arbitration-eligible.
Estrada, 30, hit .301 with 11 home runs and 71 RBIs during his only season with Arizona. The switch-hitting former All-Star had the sixth-best batting average among National League catchers.
Starting pitching behind NL Cy Young Award winner Brandon Webb was a major weakness for the Diamondbacks last season. Davis, who has thrown at least 200 innings in each of the past three seasons, joins Webb and Livan Hernandez in Arizona's projected rotation for next year.
"It's great to have another 200 innings guy to go along with Webb and Livan Hernandez," Arizona manager Bob Melvin said. "In addition, it's nice to have a quality left-handed starter, a variable we didn't have last year."
Estrada made the NL All-Star team with the Braves in 2004, when he hit .314 with 76 RBIs. He was limited to 105 games in 2005 after a collision at home plate with Darin Erstad of the Los Angeles Angels.
The Diamondbacks believe minor league catcher Miguel Montero is ready for the majors, and Chris Snyder is coming off a solid season as Estrada's backup.
The hard-throwing Aquino played parts of the past three seasons with the Diamondbacks, going 2-3 with a 4.93 ERA in 111 relief appearances. As a rookie in 2004, he had 16 saves.
Cubs -- Alfonso Soriano wants to warm up for his Cubs debut by playing for his hometown team in the Dominican winter league. "I'm going to ask permission to play for the Eastern Stars when I get back to Chicago for the press conference where they're going to introduce me next week," the slugger told the Associated Press on Friday after arriving in the Caribbean country. Soriano's eight-year, $136 million deal with the Cubs is the fifth richest in major league history. If he gets permission to suit up, Soriano would join Yankees second baseman Robinson Cano and Dodgers outfielder Matt Kemp on the Stars. The team from San Pedro de Macoris trails the first-place Cibao Giants by 4 1/2 games. Soriano said he would keep working out as an outfielder, but is willing to consider a return to second base, the position he played before joining the Nationals before last season. "I know that Chicago already has Mark DeRosa at second base, but if they want me to play second, I will," he said.