The 23-year-old spent the spring at Djurgården after being loaned out from Russian side Rubin Kazan as a result of the war in Ukraine, and has been looking for a new club address since the loan deal expired on June 30.
Haksabanovic tells Celtic's own TV channel that a dream is now coming true.
"Of course I'm very keen to play in the Champions League, it's the biggest tournament you can play in and has been a dream of mine since I was a child.
So to be able to play in it myself is very cool," says the midfielder.
Haksabanovic thus returns to the British Isles, two years after leaving West Ham where he failed to secure a place.
Haksabanovic was brought up in Halmstad and, in addition to Djurgården, has also played all-Swedish football for IFK Norrköping.
He has represented Montenegro's national team since 2017.