He died suddenly while at home with his wife on Saturday, his agent said.
The Liverpool-born actor lent his voice to children's favourite Thomas and Friends for 13 series after taking over from Beatle star Ringo Starr in 1991.
He also appeared as Mickey Startup in Auf Wiedersehen, Pet.
He starred alongside Bernard Hill and Julie Walters in the Bafta-winning 1980s series Boys From The Blackstuff, which highlighted the hardships of unemployment.
Angelis also had roles in Minder, The Liver Birds, Z Cars and Good Cop.