Showalter received a three-year contract.
"Buck has been one of the best baseball minds for the last two decades and he makes teams better," Cohen said in a statement Monday. "We have a lot of talent on this team and Buck is the right manager to take us to the next level and lead us to sustained success. I am excited he is our new manager."
Showalter, 65, takes over for Luis Rojas, who was fired after a season in which the team held on to first place for 103 days but ultimately finished 77-85 and missed the playoffs.
Showalter has been a major league manager for four teams between 1992 and 2018. He won American League Manager of the Year honors during stints with the New York Yankees, Texas Rangers and Baltimore Orioles. He also managed the Arizona Diamondbacks and has a career record of 1,551-1,517.
His most recent managerial gig came with Baltimore, where he spent eight-plus seasons from 2010 to 2018. Showalter guided the Orioles to three playoff appearances, one division title and a berth in the 2014 AL Championship Series, in which they were swept by the Kansas City Royals.
Since then, Showalter has worked as an MLB Network analyst and on Yankees broadcasts with YES. Previously, he had a similar role at ESPN.
Wired tight but with a sense of humor, Showalter is well known for his baseball acumen, dogged preparedness and meticulous attention to detail. He is already at ease in New York's large and pressurized media market, with relationships that go back decades to his time managing the Yankees.
The Mets hired new general manager Billy Eppler last month following a long search for someone to lead baseball operations under team president Sandy Alderson, and they moved fast to sign four free agents for a total of $254.5 million: ace pitcher Max Scherzer (three years, $130 million), center fielder Starling Marte (four years, $78 million), outfielder Mark Canha (two years, $26.5 million) and All-Star infielder Eduardo Escobar (two years, $20 million).
The deals were completed in the days just before baseball's labor contract expired Dec. 1, leading to a lockout that halted transactions and froze big league rosters. That allowed Eppler -- who also spent years with the Yankees, although not until after Showalter's tenure ended -- to finally turn his attention to finding a manager. Showalter becomes the fifth manager for the Mets in just over four years.
"I'd like to thank Steve and Alex Cohen, Sandy and Billy for their confidence in me to lead this team," Showalter said. "This is a tremendous opportunity and a great responsibility to represent this organization, all Mets fans and this city. I'm energized and eager to get started."
Showalter takes over a team that has endured four losing seasons in five years and 10 in the past 13. New York has made the playoffs twice in the past 15 seasons, advancing only in 2015 on the way to a World Series appearance.
Showalter, who has never won a pennant, will need to fill out his coaching staff. The Mets announced in October that Jeremy Hefner will return as pitching coach next year, but the other coaches are expected to be replaced.
Information from The Associated Press was used in this report.