Deila was handed the reins at Celtic Park earlier this month after Neil Lennon resigned last month after four trophy-laden seasons in charge of the Glasgow giants.
Collins' appointment as number two is likely to prove a popular one among Celtic supporters, with the 46-year-old having made over 200 appearances for the club between 1990 and 1996.
The former Scotland international also represented the likes of Monaco, Everton and Fulham during his playing career and has previously been manager of Hibernian and Charleroi.
Speaking on his appointment, Collins told the club's official website: "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."
Deila added: "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 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."
