Geren, 49, had a 334-376 record in four-plus seasons with Oakland, including a 27-36 mark this season that has the A's standing in last place, eight games out of first in the American League West.
Melvin, 49, is to assume managerial duties beginning Thursday in Chicago, where the A's are to begin a four-game set against the White Sox. He previously managed the Mariners (156-168) and D-backs (337-340) and was named National League Manager of the Year after piloting Arizona to a league-best 90-72 mark and the NL West Division title in 2007. He was bench coach under Bob Brenly on the 2001 World Series-winning D-backs.
"Bob's a well-respected guy around the game," Beane said of Melvin, who most recently served as a special assistant in the D-backs organization. "He's a very intelligent guy. He's got a great reputation in regards to his relationships with player. Where he takes that from here, he's got the opportunity here."
Melvin is also a Bay Area native who grew up a fan of the A's and Giants, went to the University of California and went on to play in the Major Leagues for the Giants, among 10 seasons with seven clubs as a backup catcher. He's wearing No. 6 in honor of "Captain Sal Bando of the Swingin' A's," as he said.
"For me, there is added significance, obviously," Melvin said in a press conference at U.S. Cellular Field. "This is my third managerial job, but I'm coming home to a place where I grew up, went to grammar school, high school there, went to the University of California, played for the Giants.
"I understand the history of all those organizations, especially this organization. Really, it's a dream come true. This doesn't happen very often in baseball, where you literally get to come home in the capacity that I do."
Melvin becomes the 29th manager in franchise history and 18th since the team moved to Oakland from Kansas City in 1968.
The switch was the first in-season change of managers the A's have had since Tony La Russa become the team's skipper on July 7, 1986, replacing Jeff Newman, who was interim manager for 10 games following the dismissal of Jackie Brown.
Beane previously replaced Art Howe with Ken Macha and then Macha with Geren, but those were offseason changes.
"When you replace your manager, listen, it's a drastic move no matter who's doing it," Beane said. "I've never had to do it [during the season] during my tenure here as a general manager, so this is a new script for myself. I'm not sure you ever know exactly when the right time is."
With starters Dallas Braden, Brett Anderson, Brandon McCarthy and Tyson Ross all landing on the disabled list in recent weeks -- and veteran second baseman Mark Ellis joining them this week -- the A's are dealing with injuries among other challenges that await Melvin.
"Bob Melvin will inherit some of the challenges that Bob [Geren] had," Beane said. "[Geren] lost four starting pitchers in the space of three weeks. That's a tough body blow for the team. That's a situation Bob inherits, and we certainly have to be realistic starting out of the gate how we manage around those four guys on the disabled list."
For Melvin, managing the situation means having his players focus not on those problems that face the club, but on what they can do each day.
"The focus is going to be to slow it down, back it up and play day to day," Melvin said. "Don't worry about what happened yesterday, don't worry about what's going to happen tomorrow. ... I have to adapt to the players more so than they have to adapt to me. One thing I can tell you is that there's going to be energy, there's going to be passion for what they do, and we're going to play for 27 outs."
Beane said Geren will be attending his son's graduation and spending time with his family, and that it was too soon to say whether Geren will have a role in the organization going forward.
"Any time you're letting somebody go, it's never easy regardless of the relationship, to be honest with you," Beane said. "That being said, the fact that I've known Bob a long time and we do have good communication, there was always that open line, so despite the fact from a personal standpoint you never like to see a friend lose a job, but on a professional standpoint in some respects it was easier to communicate with Bob in a circumstance like this."
That also was the case in this transition with Beane and Melvin, who had many conversations when Melvin was managing the Mariners and came to Oakland, developing a mutual respect.
"I think our relationship was how this came together so quickly," Melvin said. "It's a difficult situation, it was difficult for Billy, it's going to be difficult for everybody involved here. But I think it came together so quickly because we've known each other so long and have respect for each other and know what the other's strengths are."
Said Beane: "One of the things Bob has a great reputation for is his relationship with everybody who works around him, whether it be the front office or particularly the players. He's got a great reputation in the league from his former players, and that's important in today's game, no question about it. Those are the 25 guys you have to live with every day. He's just a very bright guy and represents sort of a modern-day type of manager."