But they also called for the Government to close the gap between rhetoric and reality and questioned how the new office would link with the department responsible for local government.
The office, which will be led by Ed Miliband, will co-ordinate the Government's approach to the sector across Whitehall.
He will report to Hilary Armstrong, Minister for the Cabinet Office.
"We're very pleased," said Stephen Bubb, chief executive of Acevo. "This was one thing we raised during our meeting with Tony Blair earlier this year."
Stuart Etherington, chief executive of the NCVO, said it was an ideal solution. "Our 2005 election manifesto called for the Cabinet Office to be given responsibility for the sector," he said.
Miliband told Third Sector that the new post reflected "the importance the Government attaches to the role of the third sector in all parts of national life".
More details of the sector's role in public service delivery will be revealed at a conference hosted by the Cabinet Secretary on 6 June.
Debra Allcock Tyler, chief executive of the Directory of Social Change, said it had "learned to be unexcited about ministerial reshuffles" and urged Miliband to close the gap between rhetoric and reality. She called for initiatives to be delivered effectively before new ones were invented.
Acevo also questioned how responsibilities would be divided between the Cabinet Office and the Department for Communities and Local Government, now led by former education secretary Ruth Kelly.
- See News Special, page 3, and Editorial, page 22.