Warner also stepped down as chairman of the National Council for Voluntary Organisations following Tony Blair's recent ministerial reshuffle, though he will stay until a successor is found.
Warner had been chair since the Youth Justice Board's inception in 1998, and his departure comes after he was recently re-appointed for three more years.
Pollard, who chairs the board's Youth Crime Prevention Committee and Restorative Justice Sub Committee, has also been a member of the board since 1998. He was chief constable of Thames Valley Police for 11 years up to February 2002.
Blunkett said: "I would like to thank Norman for the vision, commitment and enthusiasm he has brought to his role as chair of the Youth Justice Board."
The Home Secretary also announced that two other board members, Theo Mutale and Rob Allen, have been re-appointed for a further three years.
Scotching speculation that the Youth Justice Board might be absorbed into the Home Office, a spokeswoman for the department said such changes would require an amendment to the Crime and Disorder Act 1998, under which the Youth Justice Board was set up.
The National Council for Voluntary Organisations has also started the recruitment process for a replacement.
Warner was last year due to become chairman of public spending body the Audit Commission, but his appointment faced opposition and was blocked.
Under his new position as parliamentary undersecretary of state at the Department of Health, Warner will oversee NHS performance ratings, the Commission for Healthcare Audit and Inspection and quality and clinical governance (the Commission for Health Improvement).
