He is said to have grown weary of defending the company from political attacks and public outcry.
Damelin currently holds a 5% stake in the payday loan company, which is worth around £50m.
The UK payday lending sector is worth around £2bn, having doubled in value since 2008.
The FCA will take responsibility for the consumer credit industry, including payday loans, from 1 April 2014.
The authority has already warned lenders they will not be able to extend loans more than twice, while they are prohibited from repeatedly attempting to take payments from people’s bank accounts.
