Home Secretary Theresa May announced the appointment, The Daily Telegraph reported.
"Under his 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," May said. "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."
Parker, 50, has been in his current post since 2007 after heading the division in charge of counter-terrorism for two years. He has been with MI5 for 30 years.
Evans has been director general since 2007. MI5 deals with internal intelligence and counter-terrorism.
He also continues of tradition in British intelligence by being a bird-watching enthusiast. Ian Fleming, who worked in naval intelligence during World War II, named his fictional spy, James Bond, after the author of a field guide, "Birds of the West Indies."
Parker, who has a degree in natural sciences from Cambridge University, is married with two children.
Astronomers offer more expansive view of universe
Beautician charged with giving client fatal silicone butt injection