The 38-year-old takes over the hot seat at Parkhead having led Stromsgodset to the Norway League title in 2013 - their first in more than 40 years.
Deila replaces Neil Lennon who left Celtic last month after leading the Hoops to three successive titles.
In Pukki’s first taste of Scottish football last season, the Finnish international managed just seven goals in 32 appearances.
And he is pleased to welcome the Norwegian to Glasgow, saying: "It's a big thing that the manager wants to play attacking football. As a striker you always hope for a manger like that."
On his performances in the Hoops last season, Pukki added: "The first year with Celtic has been one of adapting for me.
“A lot has been different for me over the last year but the end of the season was good and I found it easier to play.
"I felt good towards the end of the season and was scoring goals and got more confidence in my play.
“I was playing well otherwise, so this was good for me as it showed what I'm capable of.”