Shaw, who has died aged 63, featured in the Aston Villa side that won the First Division title in 1981 and the European Cup the following year.
The forward, who also had spells with Blackpool, Walsall, Kilmarnock and Shrewsbury, had been in hospital after suffering a head injury in a recent fall.
In a heartfelt tribute on X, Collymore, who played for Villa after spells at Crystal Palace, Nottingham Forest and Liverpool, wrote: "Dear Gaz. I wanted to play football because of you. I love Villa because of you.
"When I was 11 I asked my Mom if I could have a blonde wedge because of you.
"Her wry, 'I don't think we can do that, son', will stay with me as one of my abiding memories of her, too.
"You were a real-life superhero.
'When he gets the ball he's bound to score', I'd sing at home, in the Holte End, when you were on telly.
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