Despite the Scottish champions' desire to secure a permanent deal for Roberts, they have been unable to match City's valuation of the player, who has been given a chance to impress manager Pep Guardiola during their pre-season tour of the United States.
Back in January 2016, the 20-year-old moved to Parkhead on an 18-month loan deal and his 11 goals in 47 appearances this past season helped Brendan Rodgers' side claim a remarkable domestic treble, having gone through the entire campaign unbeaten.
Hayes said: "This is a huge honour for me. It is a dream come true to be part of this brilliant football club and I can't wait to get started", he said.
"I'm delighted. It's been in the pipeline for a little while now but I'm pleased to finally get here". I'm delighted. Celtic have done well over the last few seasons and with the manager coming in a year ago he raised the level again.
After finalising terms to remain in Glasgow until 2020, Hayes admitted that he can not wait to get going next season. It was hard a year ago seeing all the celebrations and all the stuff on social media and you want that for yourself and to be part of it. "It was hard previous year seeing all the celebrations and all the stuff on social media and you want that for yourself and to be part of it", said Hayes to the Celtic website.
"Now it's my chance and hopefully, going forward, I can create my own little bit of history and take the chance I've been given".
"You can't get away from the Champions League".
"Whether you're a football fan or not, everybody knows about the atmosphere of Champions League nights at Celtic Park".