Myers was traded to the Reds in 1990 for closer John Franco, and became one of the league's elite closers and the most successful member of the Nasty Boys trio, which also included Rob Dibble and Norm Charlton, while being selected as an All-Star in 1990. 1990 also gave Myers his second World Championship as the Reds swept the Oakland Athletics. In 1991, the Reds experimented with Myers as a starter, a move that proved highly unsuccessful as he posted a record of 6 wins and 13 losses.
1992 found Myers back in a familiar role, but with a new team, as he became the closer for the Padres. After only one season in San Diego, Myers was a Cub in 1993 where he posted his best statistical season with a then National League record 53 saves. In a September 28, 1995 game vs. the Padres, Myers was attacked by a fan at Wrigley Field after giving up a home run. In 1994 and 1995, Myers earned his second and third All-Star selections. After the 1995 season, Myers became a member of the Orioles where he had two more solid seasons, highlighted by an All-Star selection in 1997, when he saved 45 games. Myers had 28 saves for the Blue Jays in his final season, 1998, before being traded back to the Padres after being claimed on waivers. Though he was under contract for both 1999 and 2000, he did not pitch in the Major Leagues after 1998.
In a 14-year Major League career, Myers compiled a 3.19 ERA, 347 saves, 44 wins, 63 losses and struck out 884 batters in 884.2 innings. Going into the 2008 season, Myers ranked 7th on the all-time Major League career saves list. He has since been passed by Billy Wagner of the New York Mets and Troy Percival of the Tampa Bay Rays.
In 2000, Myers earned a salary of $6,916,667.00 while unable to pitch due to a damaged shoulder. Most of his 1999 and 2000 seasons were spent receiving treatment in the Padres training room after undergoing rotator cuff surgery in 1999; his injury resulted in a legal dispute between the Padres and their insurance carrier after the carrier denied an $8 million claim due to Myers' inability to play. 
The Padres' 1998 waiver claim of Myers is considered one of the biggest blunders in the history of the waiver wire. The Padres did not want Myers, mostly because of the $12 million and 2 additional years remaining on his contract as well as the fact that they already had an established closer in Trevor Hoffman, but placed a waiver claim in order to prevent him from going to the rival Atlanta Braves. They expected the Blue Jays to rescind their waiver claim, but the Blue Jays instead allowed the waiver claim to go through, leaving them responsible for the rest of his contract.