Boswell will stand down from the institute in October and join FareShare in the same month. He has been in his present role for 10 years.
The institute will begin the recruitment process for a new chief executive next week.
Boswell told Third Sector: "I think the institute could do with a fresh perspective. Everybody has a shelf life and it’s important to keep an eye on that.
"I’m a massive fan of FareShare and the opportunity was too good to miss. My first act at the charity will be to get them to join the institute."
FareShare, which distributes food to organisations working with disadvantaged groups, won Third Sector’s Britain’s Most Admired Charity award in March.