Lyons, who was appointed chair in May 2007, made the announcement in a letter to Jeremy Hunt, secretary of state for culture, media and sport. Lyons said he was proud of the achievements made over the years.
"We have worked to shape BBC services in a way which maximises public value and secures the highest editorial standards, at the same time seeking to ensure that the BBC operates within clear boundaries and cooperates effectively with others.
"We have taken openness and transparency to a new level. Most important of all, under the Trust's guardianship – and with the leadership of the director general and his team – the quality and public service focus of the BBC's output has improved and the public's affection for the BBC has strengthened."
But, he added, the role of chairman had been "far more demanding" than the job specification had indicated.
"It is of course a compelling aspect of working at the BBC that it can become an all-consuming part of one's life – and this applies equally to the staff across the BBC whose great commitment helps underpin its position as the world's leading public broadcaster.
"But this workload has now reached a point where I am increasingly concerned that it is crowding out other appointments to which I remain committed and other activity that I wish to undertake. So balancing all the factors I have on reflection concluded that my preference would be to limit my appointment to a single term and not seek reappointment from next May."
In his letter he also pledged to continue to offer his "full energy" to issues over the coming months, such as public debate over funding of the broadcaster and its Strategy Review.
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