Coun Wakefield began to break the news to council colleagues on Tuesday and is understood to have been in contact with other bodies where he sits, such as the West Yorkshire Combined Authority, to confirm his intentions today.
He first became leader of the Labour group in 2003, serving as council leader until 2004 when his party lost power to a Conservative and Liberal Democrat coalition.
He remained Labour group leader in opposition and regained the role of council leader when the party returned to power after the 2010 elections.
Coun Wakefield has led the council through one of its most difficult periods as the authority has had to cope with huge reductions in funding from central government, forcing it to cut large numbers of jobs and radically change the way it provides services.
He has also been a key architect of efforts to get West Yorkshire councils to work more closely together and has played a pivotal role in negotiations with the Government to devolve powers and funding from Whitehall to the region.
Coun Wakefield, along with Leeds City Council chief executive Tom Riordan, was central in persuading councils in Yorkshire to back the hosting of the start of the Tour de France.
He was first elected to represent Kippax in 1988 and is expected to continue in that role after stepping down as council leader and leader of the Labour group.
He said: “Needless to say it’s always a difficult decision to make, especially given the achievements of the council and this great city since 2010 when I resumed my second term of office as council leader.
“Together we’ve made real progress with our ambition to be the best city and I know you will continue work with the council to improve the lives of everyone in Leeds.”