The 24-year-old, who trained with his parent club today, will spend the remainder of the campaign at Parkhead.
He told the official Celtic website: “This is an exciting move for me and I’m delighted to be joining a club like Celtic, which has a great reputation throughout Europe.
“I’m looking forward to meeting my new team-mates and working with the manager, and I’ll be doing everything I can to help the team to be successful in the remainder of this season.”
It is understood that there is no clause which would allow Celtic to make the move permanent in the summer.
Toljan, who can player right or left-back, is yet to feature for the first-team this season but made 23 appearances last season following his £6million move from Hoffenheim in 2017.
He was part of the Germany squad which won the U21 European Championship in 2017 and picked up silver in the 2016 Olympics.