The Manchester-born comedian passed away on Saturday at a nursing home at Rhos-on-Sea, Conwy. He had been suffering from Alzheimer's disease for several years.
Goodwin rose to fame in the 1970s through mainstream shows including Opportunity Knocks and The Comedians.
He was known for his stuttering and nervous on-stage demeanour, and for his catchphrase "Settle down now, settle down".
His former manager and close friend Clive Stock described him as "a gentle man and a gentle comedian".
The comedian's death comes in the same week as his former colleague Frank Carson, who died at the age of 85 yesterday.
Goodwin's funeral will be held at St Hilary's, Llanrhos, Llandudno, on Friday, March 2.
> Frank Carson 1926-2012: Obituary