The 19-year-old left-back has flown out to Spain to join up with his new team-mates at their pre-season training camp in Murcia.
Montgomery made 18 appearances for Celtic last season, including European games, before spending the second half of the campaign on loan at Aberdeen.
His arrival alleviates St Johnstone’s injury concerns in the left-back area with Tony Gallagher and Callum Booth unlikely to be fit for the start of the season.
Montgomery said: “This is a big opportunity for me and I will be giving it my all every day.
“Callum Davidson has displayed faith in me by bringing me to St Johnstone on loan and it’s up to me to show him what I can do.
“My aim is to play as many first team games as I can and help the team win games of football.
“The hard work has started and I want to show what I’m capable of.”