Boston city councilors approved a $2.5-million, 13-year tax break that will help a Fort Point tech start-up double the size of its headquarters.

LogMeIn will expand to 327-335 Summer St., occupying the entire 117,000-square-foot former warehouse, which is undergoing $37.7 million in renovations after it was severely damaged in a December 2013 fire.

LogMeIn currently has nearly 400 employees at its 320 Summer St. offices, where it moved from Woburn in 2013. The deal with the city will allow it to add another 450 jobs, spokesman Craig VerColen said, with occupancy beginning in early 2016.

The Boston headquarters, LogMeIn’s only U.S. facility, houses approximately half of LogMeIn’s global workforce. The company also has offices in Dublin, London, Bangalore, Sydney and Budapest. LogMeIn has projected revenues of $221 million in the current fiscal year, up from $166 million in 2013. Traditionally the company has focused on remote-access software but is expanding its presence in the "Internet of Things" sector.

Boston-based Synergy Investments and DivcoWest of San Francisco acquired 327-335 Summer St. for $11 million in May 2013.