Deila will rule on whether or not to sanction the signing of former Scotland goalkeeper Craig Gordon.
And the Norwegian coach will also give the go-ahead on who should be his assistant at Parkhead - with John Collins being hotly tipped to take over.
But the 38-year-old, pictured, has been told he has no chance of luring his protege Martin Odegaard to Glasgow by his replacement.
Deila took charge of his final match at Stromsgodset earlier this week and oversaw a 2-1 win against Haugesund.
However, he is now ready to start the next chapter of his career in this country and will get straight down to business.
Ex-Hearts and Sunderland stopper Gordon, who has not played in over two years due to injury, has passed a medical at Celtic.
Fraser Forster, who is with England at the World Cup in Brazil, is expected by many to leave during the summer.
So Deila will have to give the green light to the Scottish champions signing a player he has little knowledge of.
Meanwhile, Stromsgodset caretaker manager David Nielsen has warned Celtic fans their new manager has no chance of landing Odegaard.
The 15-year-old, who has been watched by Bayern Munich and Manchester United, made his debut for the Norwegian club in April.
That made the attacking midfielder the youngest player ever to take part in a Tippeliga match.
He scored a goal against Sarpsborg 08 FF last month to become the youngest player ever to hit the target in the league.
But Nielsen reckons the biggest clubs in Europe are ready to table bids for the precocious youngster.
Asked if Celtic could sign Odegaard, he said: "He's out of their reach. He's going to play for Barcelona."
Deila will have less difficulty securing a No.2 with former player Collins, ex-Dundee United manager Peter Houston and youth coach John Kennedy all in the frame.
But former Hibs and Charleroi manager Collins, who has been coaching with the SFA, is believed to be the front runner and has been spoken to about the position.
Meanwhile, Deila has left his former club with the declaration: "I will always be blue."
The comment was a reference to the colours of Stromsgodset where he spent nine hugely successful years at the club.
He spoke at half-time during the win over Haugesund and thanked fans for allowing him to 'grow as a person and a coach'.
Deila took the club to its first title last season in 43 years. He said: "I am an emotional person so it was difficult to hold back the tears.
"It's a happy day too, not just about sadness. It is beneficial to both parties now, but Stromsgodset is in my heart forever. I will always be blue."