Ameche was born in Kenosha, Wisconsin. His parents were Italian immigrants who came to the United States in the late 1930s, although they returned for a year to Italy during his childhood. The family then returned to Kenosha, where he attended Kenosha High School. Ameche was a cousin of noted actors Don Ameche and Jim Ameche.
Ameche may be best remembered for his role in the 1958 NFL Championship Game at Yankee Stadium, often cited as "The Greatest Game Ever Played." Ameche scored the winning touchdown for the Colts on a one-yard run in overtime as the Colts beat the Giants, 23-17. It was his second touchdown of the day as he also scored a TD on a 2 yard run in the second quarter.
Ameche finished a relatively short six-season NFL career with 4,045 rushing yards, 101 receptions for 733 yards and 44 touchdowns.