Melvin received the American League award while Snitker took home National League honors on Tuesday, courtesy of the Baseball Writers Association of America.
Snitker, 63, led the Braves to a 90-72 record in 2018. The Braves were 59-65 in his first season and improved to 72-90 in 2017, before making the 18-win jump this season.
Melvin, 57, has been a skipper for 15 seasons, spending his last eight years with the Athletics. The 2007 National League Manager of the Year and 2012 American League Manager of the Year led the Athletics to a 97-65 finish in 2018, his highest win total as a manager.
"We feel like this is just the start of something big and that's what we talk about," Melvin told MLB Network. "Obviously we lost that last game against the Yankees but we talked about this is the start of something big for us. You look around the diamond, the veterans we have, the younger players that have come up through our system."
"There is such a passion, finally for being an Oakland A in our organization. And it's really exciting to know what we accomplished this year and that these guys are going to come to spring training trying to accomplish more. Great feeling ... our organization is in a really good place right now and we have some special players."
"I'm honored and humbled to be named this," Snitker said. "It's just beyond my wildest dreams and I'm very fortunate and blessed to be here right now."