Thompson intends to leave the job that paid him £779,000 last year after steering the corporation through the London Olympics and Queen's Diamond Jubilee celebrations.
At almost eight years in the job, Thompson has been the BBC's longest-serving director general since the 1970s, but his departure was widely expected.
Earlier in the year, the BBC Trust confirmed that headhunters Egon Zehnder had been appointed to start putting in place plans for finding a successor to Thompson, who has gained plaudits for his reign at the BBC, despite various high-profile controversies.
BBC chairman Lord Patten said in an interview that the recruitment firm had begun preliminary work so that the BBC had an "intelligent view" of possible successors to Thompson.
In an email to staff today, Thompson confirmed his departure plans and said that it has been "a great privilege" to lead "the best broadcaster in the world".
He said that a specific date for his departure has not yet been announced, but he will remain in charge until coverage of the Olympics and Jubilee has been completed.
"We can address the exact date of the handover once an appointment is made," he said, adding: "I have made it clear that I want to be guided by the wishes of the Trust and of my successor, whoever that may be."
Appointed alongside Lord Michael Grade in 2004 after the damning Hutton report, Thompson was praised for restoring the BBC's reputation for quality and impartiality.
His reign has been dogged by various controversies, including the Sachsgate scandal in 2008 involving lewd messages left by Jonathan Ross and Russell Brand on the voicemail of Andrew Sachs during Brand's Radio 2 show.
But his tenure as Britain's most powerful television executive has largely been viewed as a success, and Thompson is expected to have no problems finding a new position either here or in the US, where he could most likely earn a much higher salary.
Lord Patten paid tribute to Thompson, saying that he had been an "outstanding" director general of the BBC.
"He took over during a traumatic period in the corporation's history and subsequently enhanced its reputation for creativity and quality, while setting the course for the BBC's digital future," said the BBC chairman.
"I will miss him on both a personal and professional level and I wish him the very best of luck for the future. The Trust will shortly begin the process of recruiting a successor."
The BBC could look to replace Thompson with an internal candidate, including the potential appointment of the first woman to run the BBC, with both BBC chief operating officer Caroline Thomson and head of news Helen Boaden considered viable candidates.
They could face competition from another BBC staffer in George Entwistle, who was appointed the head of TV channel division BBC Vision last year, or external candidates such as ITV's director of television Peter Fincham and Channel 4 chief executive David Abraham.