The deal came as no surprise after the news on Wednesday that Robertson had left Leicester City by mutual consent.
Though Robertson's departure from Filbert Street where he had worked alongside O'Neill had been expected for some time, negotiations between the club and the Celtic had been drawn out.
However, with Leicester releasing Robertson after four years with the Foxes on Wednesday, the Scottish giants were quick to snap up the assistant boss.
The former Nottingham Forest winger will be able to join O'Neill in the dug-out for Sunday's Old Firm clash with Rangers.
Complete the jigsaw
O'Neill was delighted to renew his acquaintance with Robertson and is hoping to continue the partnership which saw them bring success to Leicester.
"He will have a broader role in our set-up because there is much work to be done on the football side."
O'Neill and coach Steve Walford left Filbert Street for Celtic during the summer and it now Robertson has completed the jigsaw.
The trio will now look to returning Celtic to the top of Scottish football.
Robertson said: "I am delighted to be joining up with Martin O'Neill and Steve Walford again and to do so at Celtic is an honour.
"Celtic is a huge club with a legendary support and I am looking forward to working with the Celtic players and the rest of the staff here to bring them the success they deserve."
Related to this story:
Izzet stays a Fox
(21 Jul 00 | Leicester City)
Leicester's Lennon boost
(10 Aug 00 | Leicester City)
Collymore's England goal
(15 Aug 00 | Leicester City)
Vega rejects Celtic's overtures
(23 Aug 00 | Tottenham Hotspur)