Private equity group Permira acquired the firm in September, in a deal worth almost £230m.
Sixty-four-year-old Fuller (pictured), who founded the business in 2004, will remain Just Retirement’s second largest investor after Permira. He will also provide ongoing consultancy services to the firm.
Cook has held his post at LV= for the past three years. Prior to that, he worked at Prudential and Zurich.
Just Retirement recorded a 26 per cent rise in sales to £446.1m for the six months to December 2009, up from £353.9m the previous year.
The firm is understood to be striking a deal with Co-op Financial Services to provide enhanced annuities, as well as partnership arrangements with other firms.
Fuller says: “We are delighted to find somebody with the combination of experience that Rodney has.
“He is joining the business at a very exciting time. I am really enthused about how well Just Retirement is doing and about a number of major initiatives that will be coming through 2010. I also envisage we will hit the £1bn mark in sales this year.
“I am not intending to go out with a whimper. I want to go out with a bang.”