The former defender cemented himself as a firm fan’s favourite for his committed performances during an 11-year playing career with the club.
And the 43-year-old, who replaces Steve Harrison, is calling on that support once more to help push the Sky Blues back to the Championship.
“I want to urge the fans to stick with us,” said Shaw, who will join former team mates Steve Ogrizovic and Lee Carsley on the club’s coaching staff.
“They’re the most important aspect of this football club.
“As a player I received a huge amount of support from them down the years and now we’re going to need it again next season.
“It was very sad seeing the club get relegated but a lot of big clubs down the years have been in League One.
“No club has a divine right to be in any league and you’ve only got to look at the likes of Leeds, Nottingham Forest, Leicester, Charlton etc, who have all been there but managed to get out.
“It’s a very tough league but we’re going to be giving it our all for the supporters and hoping to get the club back into the Championship.”
Shaw signed from Crystal Palace in November 1995 for £1million and went on to make 362 appearances with just one memorable goal to his name – a 25-yard screamer against Gillingham in 2004.
He returns to the Ricoh Arena after a six -year spell at Millwall where he was the club’s reserve team manager since retiring as a player in 2008.
Shaw helped guide Millwall to the League One play-off finals on two occasions and he is hoping to draw on all of his experience to bring some overdue success to the Sky Blues.
“I had other offers on the table but I jumped at the chance to come back really,” Shaw added.
“The move came out of the blue really. I had a call from Andy and we know each other well from our Crystal Palace days, so it seemed like the right thing to do.
“I obviously have a good relationship with the club and supporters so this is a fantastic opportunity for me but I am under no illusions that we have a job on our hands next season.
“I spoke with Lee (Carsley) and he has told me there are some very good young players here with the right attitude coming through so hopefully we can build on that and with the right team spirit and lots of hard work.”