The 54-year-old has been at the Etihad for nine years.
Allen will play a key role in the Light Blues’ signing policy as well as being charged with reorganising the scouting and academy structures.
He said: “The time was right for me to look for a fresh challenge and I am joining one of the world’s truly great football clubs.
“Steeped in history and tradition, I am honoured to join Rangers and work with the board of directors, Pedro Caixinha, his management team and the staff at the club.”
Rangers had originally wanted to fill the role in April, but top target Ross Wilson opted to stay with Southampton.
Ibrox managing director Stewart Robertson is hopeful the months spent on the recruitment process proves to be time well spent. He said: “Mark is a man of vision who has achieved great success with Manchester City’s academy.
“He has excellent contacts in football but also the business world and he will be a great asset to Rangers.
“We said we’d not rush into an appointment as we wanted the right candidate and we feel Mark is the best man for the job. We look forward to working with him closely in the years ahead in what will be an important role at the club.”
On the pitch, Mexican pair Carlos Pena and Eduardo Herrera can officially kick off their Rangers careers.
The duo were granted work permits earlier this month but had to return home to wait for their visas, which have now been issued. All the paperwork is now in place to finalise their Ibrox moves.
Midfielder Pena, 27, is a £750,000 signing from Leon, while striker Herrera, 28, is making a £1.5million deal switch from Pumas.
Pena has already made the trip from Mexico City and both players are expected to start training with Caixinha’s squad within the next 24 hours.
The pair have already been registered for Rangers’ Europa League qualifier with Progres Niederkorn of Luxembourg.
One new signing can still be registered as a wildcard up to 24 hours before the first leg, which will be played at Ibrox on Thursday, June 29.
Meanwhile, League One outfit Charlton are ready to offer midfielder Harry Forrester an escape route from Ibrox.
The 26-year-old has no future under Caixinha and is now looking at options down south.
Championship side Preston North End are also eyeing up moves for Ibrox pair Rob Kiernan and James Tavernier.
While a deal for out-of-favour Kiernan, 26, could be struck, it may prove harder to prise away fellow defender Tavernier, 25, who is under contract for another two years and remains in Caixinha’s plans for the coming season.