"Specialist negotiators are at the scene," Northumbria Police said in a statement, adding that there were no reports of injuries.
The police said: "It is believed that all the hostages had been released and that the man concerned is the only person who remains in the building".
Police said student accommodation nearby had been evacuated and a metro station closed as a precaution.
A bomb disposal unit had also been sent to the scene "following reports that the man could be in the possession of an explosive device".
"Officers have attended and found a man armed with a knife had entered the premises and it is believed that several members of staff are being held there," police said earlier.
"It is believed the man responsible is known to the Job Centre and this is being treated as an isolated incident at this stage," police said.