A statement released by 10 Downing Street said the Liberal Democrat peer has resigned as a justice minister, and will take up the post of chair of the YJB in mid-March.
Lord McNally will take over from current chair Frances Done, who has been in the post since 2008.
He had previously put forward the government's case for abolition of the YJB in the House of Lords as part of the "bonfire of the quangos" prior to a last minute U-turn in the face of opposition to the move.
Angela Sarkis, a current member of the YJB, has been appointed as interim chair from 1 February 2014, when Frances Done leaves, until McNally takes up the post.
Justice Secretary Chris Grayling said McNally’s “wealth of experience and understanding” would be invaluable to the YJB to help young people get their lives back on track.
Frances Done said McNally has a “very strong track record” of supporting both the YJB and the interests of young people in the justice system.
“I know that he will provide excellent leadership to the YJB as it continues to drive improvement across youth justice, in the community and the secure estate.”
Penelope Gibbs, chair of the Standing Committee for Youth Justice (SCYJ), said Lord McNally will bring "authority and influence" to the organisation.
“We hope he is as feisty as Frances Done has been in fighting for the youth justice system to retain the resources it needs, and in focusing on the rights and welfare needs of children who offend and who are victims of crime,” Gibbs added.
McNally was initially elected to parliament as Labour MP for Stockport South before crossing the floor in 1981 to join the newly formed Social Democrat Party (SDP), remaining with the party until 1987 when it merged with the Liberal Party to form the Liberal Democrats.
He was appointed a life peer in 1995 and was elected deputy leader of the Lib Dems in the House of Lords in 2001.
His appointment as chair follows a period of relative uncertainty for the YJB.
The body had been earmarked to be scrapped under the Public Bodies Bill as part of a government drive to reduce the number of quangos, but was handed a last-minute reprieve in November 2011.
At the time of the reprieve the Ministry of Justice said that the YJB should be reformed to “make it more efficient and directly accountable to ministers”.
In November this year it emerged that the YJB would be brought more closely under the control of the Ministry of Justice (MoJ) following a triennial review of the quango.
