The fire broke out on the fourth floor of Telephone House in May Street just before 7.30 am.
Five appliances and an aerial ladder from stations across the city attended the scene.
Police have now re-opened May Street, Seymour Street and Gloucester Street.
However, there have been reports of traffic delays in the city centre and Albertbridge area as a result.
However, the bus lane in May Street will remain closed for a short time to facilitate emergency services vehicles.
The cause of the fire is being investigated to establish whether it was accidental or deliberate.