Nine appliances and 43 fire officers attended the scene to fight the blaze.
On arrival, fire crews discovered the fire had begun in a flat, and there was extensive smoke-logging on the fifth floor of the residential complex.
Fire crews wearing breathing apparatus tackled the blaze and rescued five adults, including a woman in a wheelchair, from the fifth floor. They led a further nine people to safety from other floors in the building.
Area Commander Chris Kerr said it was a very difficult operation. "The fire was very well developed, while some crews tackled the fire with high pressured hoses their colleagues were rescuing people from that floor," he said.
"It was a very difficult operation as it is a high rise property, there are six floors.
"The lifts were out of action so crews had to drag their equipment up the staircase and when bringing the rescued people down, including the lady in the wheelchair, they were carried down the staircase. It was an arduous situation."
He added: "Thankfully there were no injuries. The people were trapped by the dense smoke outside their flats. But once the breathing apparatus teams arrived they were quickly led to safety."
Mr Kerr praised the actions of the crews.
"Whilst all the crews from across Belfast performed very well, the first crews on the scene had a very difficult job and thanks to their calmness and professionalism those rescues were carried out very quickly."
The cause of the fire has been determined as accidental.
Mr Kerr said the person who lives in the flat where the blaze is understood to have started has been rehoused in the complex.
Ulidia House is owned by Ulidia Housing Association.
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Written by Victoria O'hara