Giovanni van Bronckhorst led his side to a 1-0 success in Eindhoven to defeat PSV 3-2 on aggregate.
It is the first time Rangers have qualified for the group stage of UEFA’s premier competition since 2010. It is also the first time Scotland has had two representatives at this stage since 2007.
Both sides will find out their opponents later today when the draw takes place in Istanbul ahead of the Europa League play-off ties with Hearts in action against FC Zurich at Tynecastle Park. If Robbie Neilson’s men progress they will compete in the group stage of the Europa League. If they don't they will drop into the Conference League.
“I would like to warmly congratulate everyone connected with Rangers on reaching the UEFA Champions League group stages," Doncaster said.
“Rangers were worthy winners over the two matches against PSV Eindhoven, and the players and coaching team deserve enormous praise for how well they have performed in European competitions in recent times.
“It is great to have two Scottish clubs back in the Champions League group stages in Rangers and Celtic for the first time since 2007/8 and it will be a real benefit to the country’s UEFA coefficient.
“I would also like to wish the very best of luck to Heart of Midlothian ahead of the club’s UEFA Europa League play-off second leg against FC Zurich tomorrow.”