Jeremy Fleming, the deputy director-general of MI5 since 2013, succeeds Robert Hannigan, who announced he was standing down for personal reasons in January.
He will take over GCHQ, which operates Britain’s “listening posts”, at the heart of a transatlantic row with new US President Donald Trump.
Earlier this month Mr Trump claimed GCHQ had eavesdropped on him – a claim flatly rejected by the surveillance agency in a rare public denial.
Jeremy Fleming is a dedicated public servant
US National Security Agency director Admiral Mike Rogers also denied claims it asked GCHQ to spy on President Trump.
Mr Fleming is expected to visit the US very soon to smooth relations with the UK’s major ally.
He has nearly 25 years’ experience of counter-terrorism, counter-espionage and cyber security.
He served in Northern Ireland with MI5, led its preparations for the London 2012 Olympics and spent some time in charge of its technology.
Foreign Secretary Boris Johnson said: “Jeremy Fleming is a dedicated public servant whose work over two decades in the intelligence services has helped to keep our country safe.”