The 19-year-old, who recently signed a new Celtic contract until 2025, joins the Dons for the remainder of the season and goes straight into the squad for the Premiership match against Ross County on Tuesday evening.
Celtic relied heavily on the youngster in the earlier part of the campaign with Montgomery starting, and impressing, in a number of first-team fixtures due to injury problems at left-back.
He has made 18 appearances for Ange Postecoglou’s side, including six in Europe, and has also featured for Scotland Under-21s.
Aberdeen boss Stephen Glass hopes Montgomery can have a similar impact to Ryan Christie during his successful loan spell from Celtic across the 2017-18 season.
Glass said: “We’re pleased Adam has opted to join us at Pittodrie for the rest of the season.
“His arrival will provide some added flexibility to the squad as he can play in a number of positions.
“He is a player with great potential and someone who we feel will add value to the squad for the second half of the campaign.
“The club has previously enjoyed success with the loan of Ryan Christie from Celtic and we’re confident this move will be as successful.”