The former Fulham wideman spent the 2016-17 season at Parkhead and is now set to make his return to the Scottish champions.
Roberts made 60 appearances for the Bhoys in all competitions last season, scoring 17 goals and laying on 21 assists.
He even found the net against City as he scored in the 1-1 draw between the two sides in the Champions League at the Etihad Stadium.
City had hoped the 20-year-old would look to test himself abroad this term, with Nice and Girona both interested in taking him for the 2017-18 campaign.
But Roberts was always keen to return to Celtic having enjoyed playing for Brendan Rodgers's side so much as they went the whole 2016-17 Scottish Premiership season unbeaten.
Celtic booked their place back in the Champions League earlier this week with an 8-4 aggregate win over Astana, but have been handed a tough group stage draw with both Bayern Munich and Paris Saint-Germain in Group B.