The actor and singer passed away this morning (June 18), his talent agency Emptage Hallett confirmed to Wales Online.
Hibbard was best known as the lead singer of The Flying Pickets, the band he founded in 1982.
After he left the group in 1986, Hibbard had an extensive acting career, with roles in Doctor Who, Coronation Street, Emmerdale, Doctors, Welsh soap Pobol y Cwm and The Armando Iannucci Shows.
He also appeared in 1997 movie Twin Town and the following year's Rancid Aluminium.
Watch The Flying Pickets perform their 1983 Christmas number one cover of Yazoo's 'Only You' on Top of the Pops below: