Collins played for Celtic from 1990-1996, making 229 appearances, following his move from Hibernian, and went on to have successful spells with Monaco, Everton and Fulham, as well as earning 58 caps for Scotland and playing in Euro 1996 and the 1998 World Cup.
He was manager of Hibernian when they won the Scottish League Cup in 2007 and also had a spell in charge of Charleroi in Belgium in 2008. More recently he was director of football at Livingston in 2012.
Deila said: "I am delighted to appoint John to the position of assistant manager. I have had a number of meetings with John, I can see what the Club means to him and I can see the qualities that he will bring to Celtic.
"He is a first-class coach and has ideas on football which are very similar to mine so I am sure he will be a great addition to my team. He will start immediately and together we will now prepare for this first day of training next week. We have important matches in the near future so I am pleased that I have been able to secure him so quickly. Now we can get to work."
John Collins said: "It is a huge honour for me to return to Celtic, the Club which has always been such a major part of my life. I am grateful to Ronny for giving me this wonderful opportunity and I look forward to working closely with him and the players to ensure that we can continue to bring the good times to Celtic.
"I know what a great club Celtic is and I know exactly what the Club means to our fans. I will support the Manager in every way and I am sure that together with our players, the backroom staff and the fans, we can all play our part in bringing success to the club."