Joseph Corre, who co-founded the firm in 1984 with his wife Serena Rees, will remain as creative director. Serena Rees will leave the company.
Both co-founders will keep a minority share in the firm, which sells perfume and shoes as well as underwear.
The firm said the deal would help it become "the world's most dynamic luxury lingerie brand".
Agent Provocateur said the deal would not lead to any job losses.
Both Ms Rees and Mr Corre were awarded MBEs for their contribution to the fashion industry.
However, Mr Corre refused to accept his, because he said he found the then Prime Minister Tony Blair "morally corrupt".
Mr Corre, 39, is the son of fashion designer Vivienne Westwood.