The 33-year-old suspect was arrested on Saturday afternoon following an overnight manhunt.
The bodies of Caron Smith, 40, and 42-year-old Finbar McGrillen were discovered at Ravenhill Court off the Ravenhill Road.
The grim discovery was made by local police around 2.45 pm on Friday afternoon after officers were alerted by a member of the public.
Suspicions were aroused when the door to the flat was damaged and appeared to have forced open.
On arrival, officers at first suspected they were dealing with a possible burglary.
However, once inside they found the bodies of a man and woman.
Caron Smyth is believed to be from Drumaness in Co Down.
Det Ch Insp Una Jennings, who is heading up the double murder investigation, said: “We are treating this, at the moment, as a suspected domestic homicide.”
The senior detective said the exact causes of death would not be confirmed until post mortem examinations had been carried out.
Detectives have appealed to anyone who noticed anything suspicious in the area between 3 pm on Wednesday and 3 pm on Friday to contact them at Musgrave Street CID on 0845 600 8000.
SDLP south Down MP Margaret Ritchie said the news of the deaths was “very distressing”.
“The woman who was killed has family in Drumaness and, speaking on behalf of the whole community, I am sure they will rally around and provide whatever support they can at this terrible time,” said Ms Ritchie.
“Such a tragic loss is devastating at any time of the year, but it is even sadder so close to Christmas. My thoughts and prayers are with the family.”
Local Ulster Unionist Party councillor Jim Rodgers described the double murders as a “terrible tragedy”.
“This is really sad news for the families of this man and woman coming up to Christmas,” said the former Lord Mayor of Belfast.
“It is a terrible tragedy and my heartfelt sympathies go out to this family at this
“The circumstances of what happened still remain unclear but no one has the right to murder another person.
“Life has become so cheap in today’s society,” he added.