In a statement, the family said he died Tuesday from lung cancer, the South Florida Sun-Sentinel reported Wednesday.
Shaw was born in Miami and represented Broward County and part of Palm Beach County from 1981 to 2006, when he lost his seat to Ron Klein.
While in Congress, he served on the House Ways and Means Committee. He gained national attention in 1996 when he authored a bill that imposed stricter work requirements on recipients of welfare while offering childcare and job training.
He also served as an assistant city attorney for Fort Lauderdale, the chief city prosecutor, an associate municipal judge and city commissioner before being elected mayor of Fort Lauderdale in 1975.
Shaw is survived by his wife, Emilie; four children and more than a dozen grandchildren.
Funeral arrangements are pending.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Jordana Brewster on Paul Walker: 'He was an enormous presence in my life'