Office space covering 7,150sq m will be available on Southwark Street this year.
The Cooper & Southwark office scheme is due for completion by the end of 2017, developer HB Reavis has announced.
The building was acquired by the developer in April 2016 from Aberdeen Asset Management for £44 million.
HB Reavis started work during the summer to extend the nine-storey office block adding additional floor space, terraces on the top three floors, and a new self-contained unit on Great Guildford Street.
The scheme has been designed by Tate Hindle Architects and is close to London Bridge, Tate Modern and Borough Market, also providing transport connections to Blackfriars and Waterloo stations.
The name Cooper & Southwark is a reference to the history of barrel making that was once common in the area – a cooper is a professional maker who crafts wooden vessels bound together with hoops, such as casks, barrels and buckets.
"We've already surpassed one degree of global warming," said Kristen Buida, manager of the London Climate Change Partnership.