Randolph, 50, a major league player from 1975 to 1992 and a coach with the New York Yankees for the past 11 years, moves into his first managing job.
"This is a dream come true for me," said Randolph, who replaces Art Howe.
Texas batting instructor Rudy Jaramillo and Terry Collins, who managed both Houston and Anaheim, had also been considered for the job, which went to Randolph Wednesday.
Randolph, a second baseman, spent most of his playing career with the Yankees, but finished it as a Met in 1992.
He won six World Series rings as a player and coach.
"I'm excited," Mets catcher Vance Wilson after Randolph was hired. "The fact that he's come from a winner and learned under a guy (the Yankees' Joe Torre) who has handled situations and players and always come out on top is important. Winning breeds winning, and he can bring that over here and help get us out of the funk we're in."