Gase went 23-25 during his three seasons as head coach of the Dolphins, beating the Jets in five of their six meetings.
The Jets reached out to Gase as soon as he was sacked by the Dolphins. He is set to become the first Jets head coach with previous National Football League head-coaching experience since Bill Parcells was hired by the franchise in 1997.
During this hiring season, the Dolphins have been the quietest among the eight teams that are or were looking for new head coaches.
Rhule is a native New Yorker, who spent one season as an assistant offensive line coach with the New York Giants in 2012. The former first-round pick threw for 2,865 yards, 17 touchdowns and 15 interceptions in 13 games during his rookie campaign.