Leather will leave her current job as chair of the Human Fertilisation and Embryology Authority to take over from Geraldine Peacock on 1 August.
Stuart Etherington, chief executive of the NCVO, said he looked forward to working with her "to ensure public trust in the charitable sector is enhanced".
Debra Allcock Tyler, chief executive of the Directory of Social Change, urged Leather to "continue on the bold and innovative path" by pursuing impact, effectiveness and championing the public interest.
Kevin Curley, chief executive of Navca, said he hoped she would "probe the status" of charities set up by local authorities to deliver public services. Others said she should keep her nerve under tabloid criticism.
Leather said she was attracted by the championing role and liked the sector because it was "at the sharp end of public debate".
- See News special, page 3.