The Movie House Cinema in the city centre will close on Sunday, 26 April.
Belfast-based software company Kainos has bought the Bankmore Square site for more than £7m last year.
It plans to turn it into its new Belfast headquarters and has planning permission for a 250,000 sq ft (23,226 sq m) Grade A office building
Movie House managing director Michael McAdam said: "It's the end of an era on the Dublin Road".
"We were moved by the many stories people shared with us about their visits to the Dublin Road cinema and we know it was an important part of the local community," he said.
All staff have been offered employment at its other cinemas.
Kainos currently employs more than 1,400 people across 12 offices in Europe, the US and Canada.
It plans to move into Bankmore Square in Spring 2021.