Williams joined the coaching ranks in 2010 as the team's first-base coach under then-manager A.J. Hinch.
The following season Williams was moved to third base on manager Kirk Gibson's staff and remained there for the next three seasons while also working with the team's infielders.
"I'm bummed that we won't have him anymore," second baseman Aaron Hill said. "But I'm very excited for him and his family. Matt has been one of the favorite coaches I've ever had. I've learned so much just in the short time I've been with him."
Williams was a hard-nosed, fiery player, but since becoming a coach, he has impressed those in the Arizona organization with his ability to stay calm and focused regardless of the situation.
A case in point came during the melee between the D-backs and Dodgers in June, when Los Angeles hitting coach Mark McGwire became so enraged that he grabbed Williams by the jersey with both hands and yelled in his face.
While McGwire drew a suspension for his actions, Williams drew praise from those in baseball for the fact that rather than escalate the issue, he calmly talked to McGwire while preventing him from entering the scrum.
"You hate to lose someone that is that valuable, but on the other hand, and I don't want to put words in the organization's mouth by any means, but I would be hard-pressed to find anyone who is not happy for him," veteran shortstop Willie Bloomquist said. "Just because you could see the path he was going, that he was going to be a manager."
Williams managed Arizona's Double-A Mobile team on an interim basis for the final two months of the 2007 season and he skippered the Salt River Rafters of the Arizona Fall League in 2012, a team that included Nationals and D-backs prospects.
"As far as just baseball smarts, he's just very, very knowledgeable about the game," Bloomquist said. "In all facets and all areas of it, he's extremely knowledgeable. ... He anticipates things and has an idea about what's going to happen and is just a smart baseball guy."
Williams nearly landed the Rockies' managerial job last offseason, and as the 2013 season wore on and his name came up in connection with the Nationals, players in the Arizona clubhouse dreaded the thought of losing him.
"He will be a great manager and continue to be a great mentor," Hill said. "I can go on and on about the guy. He's awesome."
During his playing career, which stretched from 1987-2003 and included stints with the Giants, Indians and D-backs, Williams was known as an old-school player, who disdained showboating.
While still leaning toward that end of the ledger, he has adapted to the times. Rather than talk about how things were during his playing days, he has realized the challenges today's players face.
"He's a realist, he understands that the game is changing constantly and it's becoming more and more difficult, and he relates extremely well to players," Bloomquist said. "If I was kind of in a fielding funk, or even sometimes if my swing didn't quite feel right, he would just have one little thing that would immediately get me right back into rhythm. He was very good at doing stuff like that, and that, to me, is a sign of a great coach. He's very smart and very good at what he does, and this is just the next step to become manager. He's ready for it. In my mind, he's going to be an outstanding manager."