[3] Noonan was selected by the Dallas Cowboys in the first round (12th overall) of the 1987 NFL draft,[4] with the intention of being the eventual successor to All-Pro Randy White and to help revitalize an aging defensive line.

[5] After having the longest holdout by a rookie in franchise history at the time,[6] he fell behind in learning the nuances of head coach Tom Landry's flex defense and was only a situational player.

Against the Atlanta Falcons, he intercepted a pass tipped at the line of scrimmage and returned it 17 yards for a touchdown and sacked quarterback Chris Miller for a safety.

[7] He was released after starting the first 2 games of the 1992 season on September 14, to make room for Russell Maryland upon his return from a toe injury.

On September 16, 1992, he was claimed off waivers by the Green Bay Packers, played 6 games as a backup in the team's 3-4 defense and recorded 4 tackles,[9] before being waived on November 10.

[11] Noonan married his wife Julie in 2002 and they have six children (Sydney, Sam, Maverick, Alec, Branson and Marisa) and grandchildren Levi & Charles.