Viola, 53, spent the past two seasons as the pitching coach at Class A Savannah, following a year in the same role at Class A Brooklyn. A former American League Cy Young Award winner for the Twins in 1988 and a three-time All-Star, Viola won 20 games for the Mets in '90. He finished his career 176-150 with a 3.73 ERA.
Over the past three years, Viola has tutored such Mets pitching prospects as Rafael Montero and Jacob deGrom. In Las Vegas, he should play a significant role in Mets No. 1 prospect Noah Syndergaard's development.
The 51s originally announced in December that Backman would return for another season as the Triple-A manager.
"I'm excited to return to Las Vegas for my second season," Backman said in a statement. "I'm also excited about the fact that we will have a solid team to start the season and our pitching has the potential to be better than last season. Our players did a good job getting a grip on it quickly in regards to adjusting to the [Pacific Coast League] and knowing what the main goal is while playing in Las Vegas."
Anthony DiComo is a reporter for MLB.com. Follow him on Twitter @AnthonyDicomo. This story was not subject to the approval of Major League Baseball or its clubs.