The research centre will be built in Harley street after the plans were approved by Westminster City Council.
There were concerns by residents that living near the centre may cause radiation dangers. as well as distruption.
Deputy Conservative council leader Robert Davis said “additional conditions” and the council’s new construction code of conduct would “mitigate the impact of this development on the local community”.
He added: “I can think of few better reasons to approve a development than creating a centre of excellence where people receive high quality medical care and attention, particularly for the treatment of an illness that affects so many of us.”
A letter from neighbours claimed experts had said there is insufficient information “to be able to comment on either the viability or safety characteristics” of the technology.
Simon Baynham, of Howard de Walden Estates, has previously said: “This Harley Street facility will make an important contribution to the advancement of next generation radiotherapy to the UK and carries no noise/radiation exposure/vibration risk.”