Leeds-based Zenith said Lord Rose has over 40 years’ experience in the consumer and retail sectors during which time he has served as chief executive of M&S, Argos, Booker and Arcadia Group.
Lord Rose is taking on the position in addition to his roles as chairman of online grocer Ocado and retailer Fat Face.
The appointment comes after Zenith was snapped up by private equity group Bridgepoint in a £750m deal in January.
Lord Rose said: "I am impressed by Zenith's growth story. The UK fleet services market is a large, growing and resilient market so we will all have even more to go for."
Zenith was launched in 1989 and focuses on funding company cars and commercial vehicles.
Chief executive Tim Buchan added: "I'm delighted that Stuart is joining Zenith as our chairman.
"He's had a fantastic business career and has unparalleled experience in understanding the consumer, all of which will be important to the future development of our company."
Mr Buchan said that as Zenith grows, it needs to think more like a retailer and that is where Lord Rose's expertise will come into play.
"The big opportunity for us is to develop a one-stop shop that covers very large trucks, through to vans, through to cars and then to fork lift trucks," he said.
"Big infrastructure companies need a one-stop shop and no-one in the market can provide that."
He said Lord Rose will work the hours he is required to work, rather than work a pre-arranged number of days.
"If we are making acquisitions, he'll spend more time with us. We are always looking at acquisition opportunities, but our main focus is on organic growth."
He said that most large corporates are being very careful about further investment as they work out how Brexit will pan out.
"We have to continuously grow and invest in the business," he said.
Zenith is investing heavily in its new headquarters at No.1 Kirkstall Forge to create a visionary and contemporary workspace over three full floors, within the new building.
Zenith plans to relocate to the new offices before the end of the year.
Ultimately, the scheme will include 1,050 new homes, 300,000 sq ft of offices and 100,000 sq ft of retail, leisure and community space.
Lord Rose, who helped spearhead ex-prime minister David Cameron's campaign to remain in the European Union, was knighted in 2008 after holding a string of prominent retail jobs.
He almost came to blows with Sir Philip Green over the retail tycoon's ill-tempered bid for M&S in 2004.
He was chairman of Marks & Spencer from 2008 to 2011. He was knighted in 2008 for services to the retail industry and corporate social responsibility, and granted a life peerage in August 2014.
Lord Rose is also a non-executive director of South Africa-based Woolworths Holdings and a member of Bridgepoint's advisory board.