Alex Younger said UK intelligence and security services had disrupted 12 terrorist plots since June 2013.
He said many of the threats came from ungoverned spaces in the Middle East - namely Iraq and Syria.
Mr Younger also warned that "hybrid warfare", which included cyber-attacks and subverting democracy, was becoming an "increasingly dangerous phenomenon".
"The risks at stake are profound and represent a fundamental threat to our sovereignty," he said. "They should be a concern to all those who share democratic values."