Wrexham have splashed out £7.5m for Doyle, with City retaining a 25 per cent sell-on fee.
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"I think Callum was at the stage in his career where he's ready to find a home. He'd had a lot of loan moves and (wanted to) be part of something," said Parkinson.
"He's a player in demand. We've genuinely had to compete with some really good clubs to bring him here. I think he's a player of huge potential and it's a good signing for us.
"I think it is a statement of intent that we've won his signature over some established Championship clubs, who've been in the division and Premier League recently, and clubs in other European leagues."