Andrew Parker will take up his new role on Monday, April 22. Cabinet Secretary, Sir Jeremy Heywood, said:
"He brings his deep knowledge and experience of all aspects of the Service and its operations to this role and will be a great leader of the Service, working collaboratively with its partners. I look forward to working with him in his new role.
"I would also like to pay tribute to the outstanding way in which Jonathan Evans has led the Service since 2007 and I wish him all the very best for the future."
New leadership to 'maintain global reputation' of MI5
Under his [Andrew Parker's] leadership the Service will continue to stay ahead of global and domestic threats to our national security and further develop its reputation as one of the world's most effective security agencies.
I also pay tribute to the work of Sir Jonathan Evans, who has led the Service through challenging times of change and unrest, including in the aftermath of the 7/7 London bombings. His tireless work also helped ensure the delivery of a safe and successful Olympic and Paralympic Games last year.
Cyber attacks 'cost UK economy billions each year'
Cabinet Office Minister Francis Maude has warned that cyber attacks cost the UK economy billions of pounds each year.
Speaking on the launch of a new security cell to combat cyber attacks, he said the government intends to make Britain one of the safest places to do business in cyberspace.
Mr Maude said: "We know that cyber attacks are happening on an industrial scale and businesses are by far the biggest victims of cyber crime in terms of industrial espionage and intellectual property theft."
Security cell launched to combat costly cyber attacks
The government has formed a security cell comprising experts from MI5, GCHQ and the private sector to combat the growing threat from cyber attacks.
There will be around 12-15 analysts working for the so-called "fusion cell" from a secret location in London.
The cell is part of the Cyber Security Information Sharing Partnership, which has grown out of a pilot project last year whereby 80 companies shared information about cyber threats and methods of countering them.
Under the partnership, companies will have access to a web portal, described as being "like a secure Facebook", for sharing intelligence.
Cyber attacks are a growing problem, not just in terms of national security but also industrial espionage and intellectual property theft among British businesses.
MI5 boss thanked for 'invaluable contribution to public safety'
Speaking at Home Office questions in the Commons, Theresa May said: "He has experienced the service evolving over the years and as Director General has lead the service through particularly challenging times of change and unrest, including the aftermath of the 7/7 bombings.
"His tireless work helped ensure the delivery of a safe and successful Olympic and Paralympic Games last year.
"I commend and thank him for his invaluable contribution to public safety and national security."
Shadow Home Secretary Yvette Cooper said: "We also give thanks for the work Sir Jonathan Evans has done over many years for the security of this country."