The charity is seeking an interim director to replace him before making a permanent appointment.
Burne said: "I am really looking around and have not made fixed plans yet. I am probably going to move into consultancy work for a bit. We've just decided to go our separate ways. I wish NCH all the best for all it does in the future."
He will also vacate his position at the institute in July after two years as chair and six as a trustee. "You can only stay as trustee for six years and I'd already done three and a half when I accepted the chair," he said.
During his tenure at NCH, Burne reversed a long-term stagnation in income, and increased net income by 24 per cent and gross income by 12 per cent by reducing costs. The charity is expecting similar growth this year, said Burne.
He also increased the charity's revenue from share giving from £600,000 last year to £2m this year. He said: "It is an extraordinarily tax-efficient form of giving for major donors, much more than payroll giving, and it is far more simple."
NCH has focused mainly on the Alternative Investment Market for its share gift donors, particularly around the launch of new companies on the market, he said.
Before joining NCH last year, Burne was director of fundraising at the Acorns Children's Hospice. Until 2000, he was head of central fundraising at the Children's Society, where he pioneered face-to-face fundraising, and before that was director of fundraising at Relate, where he doubled the project income.
His first voluntary sector role, aged 22, was with VSO in Papua New Guinea.