Majstorovic has secured his release from the final year of his contract with Greek club AEK Athens and is now primed to join Celtic.
He is likely to undergo a medical on Saturday and the 33-year-old is expected to sign a two-year deal with Neil Lennon's side.
"I had two wonderful years in Greece with AEK and I am very happy to have the chance to play for such a big club," said the centre-half.
"I would like to thank the fans and all the people of the club.
"For me, Celtic is a big European club and a good chance to play football at a high level.
"I will travel on Saturday to Glasgow in order to have the medicals and to put my signature on the paper."
Majstorovic has also played for the likes of Malmo, FC Twente and Basel earlier in his career and will help to boost Lennon's defensive options at Parkhead.