The centre's debt of about $500,000 would be taken over by RFA.
Mr Atkinson said the centre had always presented an ambitious public programme but being a stand-alone operation had become too tough in an increasingly tight and difficult market.
As part of the council's $968 million portfolio of venues, the centre would get access to a different range of show promoters as well as wider opportunities to host conventions and conferences.
It would get new paint and carpet and its running costs would fall as regional facilities provided back-office support.
Three of the staff were offered roles with regional facilities or help to find jobs, and two others had resigned.
Devonport-Takapuna Local Board member Jan O'Connor said the board gave the centre grants to put on free concerts for the elderly - including by the Navy Band - and they were packed out.
"It's a sad day for the North Shore's Town Hall and hopefully it will get back on its feet," she said.
"But we do not want its hire to be priced out of the reach of community organisations wanting to use it."
The 1100-seat theatre and conference centre was opened in 1996 and named after the playwright who grew up in Takapuna. Free performances of his The End of the Golden Weather are a Christmas tradition at the town's beach.
Land and buildings were transferred from the former North Shore City Council to the Auckland Council in late 2010, but the centre stayed under trust board control.
Bruce Mason Centre
1996 opened as council facility, run by a trust board
1164 seats
2 million visitors
200 performances
9000 meetings, conferences, dinners