The Brewers are confident Gonzalez will pass his physical because he was healthy enough to play at the end of the Venezuelan Winter League seasons.
"We don't anticipate any problems," Melvin said.
The team will have to clear a spot on its 40-man roster for Gonzalez when the contract is official.
Gonzalez, who turns 36 next month, played 24 games for the Brewers last season before tearing the ACL in his right knee on May 5 in San Francisco, an injury that required season-ending surgery. Before he was hurt, Gonzalez batted .259 with four home runs and 15 RBIs and quickly emerged as a clubhouse leader.
Gonzalez did most of his post-surgical rehab at home in Miami but maintained regular contact with Brewers medical director Roger Caplinger and other team doctors well into the offseason. At some point, Gonzalez was released from the Brewers' care.
Gonzalez's return prompted some Brewers players to take to Twitter.
"Pumped to get Alex Gonzalez back!!" Tweeted left-hander Chris Narveson soon after the deal went public. "Great teammate and clubhouse presence."
Wrote catcher Jonathan Lucroy: "Gonzo's coming back! Guy's a stud shortstop."
Brewers officials had been clear for months about their desire to bring back Gonzalez, but he initially sought a situation that guaranteed him more playing time. The Brewers made clear to Gonzalez and Eric Goldschmidt, his recently rehired agent, that the initial plan has Gonzalez coming off the bench.
In that sense, his deal with the Brewers could mark a new phase in a career entering its 15th Major League season. Gonzalez has appeared in the field in 1,536 big league games, all of them at shortstop and 1,504 of them as the starting shortstop, but he manned third base last month in Venezuela and could also see action for the Brewers at second as a backup to Rickie Weeks and perhaps even at first base, where Mat Gamel is expected to spend the first two months filling in for the injured Corey Hart.
Most importantly, Gonzalez would represent experienced insurance for Segura, who turns 23 on March 17 and was the centerpiece of the three-player package sent by the Angels to the Brewers for Greinke. Segura appeared in 44 games with the Brewers late last season and batted .264, collecting six of his seven extra-base hits in his final 21 games.
The addition of Gonzalez would not bode well for such players as Jeff Bianchi, who appeared in 33 games for the Brewers last season, and Bobby Crosby, the former American League Rookie of the Year who signed a Minor League deal with Milwaukee and will attempt a comeback after two years away from the game.
Also Tuesday, the Brewers were awaiting a decision from first baseman Lyle Overbay, who was weighing offers from several teams. The Brewers have offered Overbay a Minor League contract with an invitation to big league Spring Training camp.
Overbay, who turned 36 on Monday and split the 2012 season between Arizona and Atlanta, was with Milwaukee in 2004-05 before Melvin traded him to Toronto and opened first base for a top prospect named Prince Fielder.