Davis, along with pitcher Dana Eveland and outfielder Dave Krynzel, was part of a six-player deal with the Brewers in November in exchange for catcher Johnny Estrada, pitcher Claudio Vargas and reliever Greg Aquino.
"We believe that trading for Doug and signing him to a three-year contract improves and stabilizes our rotation," general manager Josh Byrnes said in a statement. "It is challenging to acquire and retain quality starting pitching, and this is an important step for us to build a playoff-caliber rotation."
Davis asked for $7.5 million from the D-backs, while the organization offered $5.25 million, marking the second-largest difference between a player and team. Carlos Zambrano and the Cubs were $4.475 million apart. Davis, who owns a home in nearby Scottsdale, Ariz., made $3.6 million last year.
"In the free-agent market, I could probably have gotten a lot more, but at the same time, I'm going to pitch better and my mind is at ease when I know I'm going to be in one place for three years, hopefully," Davis said in a teleconference with reporters Friday afternoon. "I'm going to be able to concentrate on pitching and pitching well and not worry about being a free agent. I think I'm going to do better in that situation."
Davis joins a rotation featuring 2006 National League Cy Young Award winner Brandon Webb, Randy Johnson and Livan Hernandez. The four veteran pitchers will provide the rotation with some depth and consistency, while the last spot will likely come from a group of youngsters in Enrique Gonzalez, Edgar Gonzalez, Micah Owings, Eveland, Evan MacLane and veteran Juan Cruz.
"I think it takes a lot of pressure off of me from where I was in Milwaukee, having [Webb, Johnson and Hernandez] ahead of me," Davis said. "I'm happy to be a part of it, also. [The pitching staff has] big names, Cy Young Award winners. I'm honored just to be on the same staff that they're on.
"As long as everybody stays healthy, I think [we will be] at the top of the league."
Last year with Milwaukee, Davis went 11-11 with a 4.91 ERA in 34 starts over 203 1/3 innings pitched, marking his third consecutive 200-plus inning season.
Although Davis' walks, hits and ERA totals have risen over the past two seasons, the D-backs are counting on him returning to his 2004 form.
"I think we expect the same kind of Doug Davis season [as in 2004], and maybe with a little better luck [and] a better defense behind him, the ERA drops down a little bit," Byrnes said in November shortly after the deal was completed.
"Davis is a guy who is an innings-eater, who is left-handed, which is something we've been looking for," manager Bob Melvin, who did not have a left-hander in the rotation last year, said shortly after the trade. "Along with Webby and Livan, he gives us another proven guy who should provide innings."
The only D-backs player yet to reach an agreement is outfielder Eric Byrnes, who asked for $5 million, while the team countered with $4.25 million.
Lindsey Frazier is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.