Wanless will leave the BLF in early June, after five years in the role.
He replaces Andrew Flanagan, who announced last year that he would stand down in March for personal reasons after four years at the charity.
In a statement, Wanless said the decision was "an unexpected move", but he wanted to lead the NSPCC "at a critical moment in the nation’s effort to eradicate child abuse and neglect".
"I am immensely proud of what we and the projects and communities we support at the Big Lottery Fund have achieved over the past five years," he said.
"My successor will lead an exciting and impactful organisation, one with good at its heart, with dedicated people, and one that is delivering something very positive for people and communities across the UK every day."
During 2011/12, the children’s charity’s income fell by £12.9m to £135.7m from £148.6m in 2010/11, which was put down to reduced income from statutory sources and fundraising events.