The long-serving controller, who was also in charge of BBC 1Xtra and the BBC Asian Network, broke the news in an e-mail to staff this morning.
Parfitt wrote: "I am immensely proud to have held this position and I leave with all three stations in great shape with their listening figures at record highs and following a great BBC-wide Glastonbury event.
"I'm most proud of the incredible teams I'm leaving behind - a group of talented, hard working, creative and inspirational people who are a credit to the BBC."
Radio 1's breakfast show host Chris Moyles told listeners: "What a shock... It's really sad for us. Our boss is going, our mate is going, you know?
"Boy, have we had some interesting times over the years!"
Parfitt has defended Moyles in the face of media controversy, describing him as a "gifted broadcaster" who "occasionally steps over a line" last year.
He also supported Moyles and his breakfast show team when they broke a world record for Comic Relief in March 2011.
Parfitt joined the BBC in 1980 and started working for Radio 1 in 1993, when he became assistant to then-controller Matthew Bannister.
He oversaw the launches of BBC 1Xtra in 2002 and Radio 1's Big Weekend in 2003, and ultimately became the BBC's controller of popular music in December 2008.
The BBC's director of audio and music Tim Davie said: "Andy has been a fantastic controller and leaves Radio 1 in rude health - with distinctive, high quality programmes and record listening figures - having transformed the station into a fully interactive digital proposition."
BBC Radio 1 and 1Xtra's deputy controller Ben Cooper will take over as acting controller of both stations while Davie oversees the process of appointing a replacement.
Bob Shennan, who is controller of BBC Radio 2, will take over Parfitt's responsibilities for popular music and the BBC Asian Network.