Viola, 50, will coach professionally for the first time since retiring from baseball in 1996. In parts of three seasons with the Mets over a 15-year career, the 1988 American League Cy Young Award winner was 38-32 with a 3.30 ERA.
At Brooklyn, he will serve under Rich Donnelly, who was named the Cyclones' manager. Donnelly, 63, has spent more than 30 seasons as a professional coach, most recently working as a roving instructor for the Pirates. Donnelly will replace Wally Backman, who was promoted to manage Double-A Binghamton.
The Cyclones also named former Cyclones player Bobby Malek hitting coach.
"We are excited to welcome our new staff to MCU Park," Cyclones general manager Steve Cohen said in a statement. "It's a wonderful thing to have a Cy Young Award winner like Frank Viola guiding our young pitchers, and we look forward to a great 2011 season with all of our coaches."
In addition to Viola and Backman, former Mets players Tim Teufel, Mookie Wilson, Howard Johnson, Randy Niemann, Keith Hernandez and Ron Darling all have jobs in the organization or with the team-owned SNY cable network.