Only a last-minute hitch will prevent the 38-year-old Norwegian being presented to the public at Parkhead.
Chief executive, Peter Lawwell, flew to Norway yesterday to hammer out the deal to bring Deila from Stromsgodset.
Compensation for the remainder of his contract - worth £200,000-per-year and which was set to run until the end of 2016 - was the major stumbling block as Deila's agent, Tore Pederson, had been in Glasgow earlier in the week to negotiate personal terms for his client. Deila flew back to Glasgow with Lawwell and, when everything is officially signed and recorded, is expected to meet the press and the supporters at Celtic Park today.
One of the first questions he is sure to be asked is who he plans to bring in as his No.2. Johan Mjallby and Garry Parker, Lennon's assistant and first-team coach, have both left.
John Collins has been in informal talks with Celtic officials about joining the backroom team. But, no offer has yet been made to the former Hoops midfielder, who has managerial experience at Hibs and Belgian club, Charleroi, and is currently working part-time for the SFA as a youth coach.
Collins' knowledge of the Scottish game, and the players involved in it, would be considered a huge asset to Deila.
The bulk of the Celtic players - with the exception of those involved in the World Cup finals - Efe Ambrose, Fraser Forster and Emilio Izaguirre - are scheduled to return from their summer break on June 24, and head off to their training camp in Austria four days later.
By then, they will know who they will face in their first competitive match, the second qualifying round of the Champions League on July 15 or 16.
Deila will need to move quickly to assess his squad and identify the players he wants to bring in. He is expected to use his knowledge of the Norwegian league - where Stromsgodset's exceptionally-young side won the title in November last year - to utilise the budget waiting for him at Parkhead.
Stefan Johansen was bought from Stromsgodset in January for just £2million, and has proved a huge hit in the Hoops midfield. Reports indicate Deila's first signing could already be on his way.
Former Scotland keeper, Craig Gordon, is set to undergo a medical before signing a short-term contract. He has not played a competitive game for two years, and had his contract at Sunderland ended after a serious knee injury.
The 31-year-old - who also broke an arm after moving to England in a £9m transfer from Hearts - has refused to accept his career is over and has fought back to fitness, training with both Dumbarton and Rangers.
Gordon - who has not given up hope of adding to his 40 caps - had been linked with the Hoops when Lennon was still in charge, and now his opportunity appears set to arrive.