The S2 building for the tech company, which will be located behind Central Saint Martins arts college, was granted the go-ahead by Camden Council last week.
Mossessian Architecture's design features a large roof terrace complete with views over London, and is expected to be completed by 2017 at the earliest.
Although it is unclear at what Google will use the building for, or how many staff will be based there, Techworld reports that the company has agreed a 15-year lease for S2 at around £55 per square foot.
"We are very excited to be moving forward with a successful planning permission for S2, a Mossessian Architecture and Argent development building," said Joe Borrett, Google's director of real estate and construction in a statement. "This achievement further cements Google's expansion in King's Cross and that Google sees King's Cross as its future home for Google London."
In January 2013, Google announced its intentions to build a new £1 billion UK headquarters in the area by 2016, although building work for this property is yet to begin.
AHMM submitted plans for the companies headquarters in 2013, but reports in 2015 stated Google was considering scrapping the London-based firm's design after CEO Larry Page allegedly branded the scheme "boring".
British designer Thomas Heatherwick was then rumoured to be working on the project – although the studio refused to comment, they did not deny the rumours. "We're not making any statement at the minute," a spokesperson told Dezeen at the time.
Despite the delay of the headquarters, Google has been quietly begun occupying several other plots in the King's Cross area.
DeepMind, an artificial intelligence startup acquired by Google in 2014, has a relatively secret office in King's Cross that accommodates over 150 people at 7 Pancras Square.
The tech giant has also taken out a lease on the neighbouring 6 Pancras Square building — and is due to start moving in up to 4,000 people within the next few months.
Google's current office in Covent Garden was designed by PENSON and features Union Jack flags and vegetables allotments, while its Victoria headquarters by Scott Brownrigg contains dodgem cars, red telephone boxes and beach huts.
King's Cross is currently undergoing a major redevelopment involving housing, shops, restaurants and public spaces. Some of the additions include the Central Saint Martins campus by Stanton Williams and a fresh-water bathing pond by Rotterdam studio Ooze Architects and Slovenian artist Marjetica Potrč.
Architect Peter Cook recently attacked the regeneration scheme, describing it as "boring, unbelievable, really dour". He went on to say he was "embarrassed" by the standard of development on the 67-acre-plot during his talk at World Architecture Festival 2015 in Singapore.