The centre-back was in Glasgow on Thursday to complete the final details ahead of his €8million move from Toulouse.
Hoops boss Neil Lennon confirmed that he hopes the player will join the club in Austria for their pre-season camp ahead of the Champions League qualifiers on Saturday.
With Jullien set to sign, attention is set to turn to Northern Ireland defender Paddy McNair.
The former Manchester United man is expected to leave Middlesbrough this summer.
However, Celtic face competition from Premier League newboys Sheffield United as well as a number of Championship clubs.
Lennon confirmed the club's interest in the 24-year-old who can also play in midfield and are preparing a £5million bid, according to the Daily Record.