Davis, 31, was 11-11 with a 4.91 ERA in 2006, the third straight season in which he worked more than 200 innings. He joins a Brewers rotation that includes National League Cy Young Award winner Brandon Webb and veteran Livan Hernandez.
"Davis is a guy who is an innings-eater, who is left-handed, which is something we've been looking for," said Diamondbacks Manager Bob Melvin, who had no left-handers in the rotation last year.
Eveland, 23, was the Brewers' 16th round selection in the 2002 First-Year Player Draft. He was 0-3 with an 8.13 ERA in nine appearances with Milwaukee in 2006.
Krynzel, 25, hit .231 with 17 doubles last season in Triple-A.
Estrada hit .302 with 26 doubles, 11 homers and 71 RBIs in 2006. Aquino was originally signed as a 16-year-old shortstop in 1995 before being converted as a pitcher. Vargas was claimed off waivers from the Nationals in June 2005.
2014: The Year in Music [PHOTOS]