Christine Day, who stepped down as chief executive of lululemon athletica this month, has already lined up her next gig–CEO of a startup that sells healthy prepared foods and is backed by Derek Jeter and Jennifer Garner.

The company, Luvo, sells items like Orange Mango Chicken with Whole Grains, Kale and Broccoli through 5,000 supermarkets. It is also testing its products in a half a dozen hospital and corporate cafeterias, and plans to open a stand-alone quick service restaurant this spring.

It is one of a number of startups that are taking aim at the supermarket industry, where many aisles are still dominated by the canned and packaged foods developed decades ago. Investors are betting that shoppers are more aware of what goes into their food and will pick better alternatives if available.

“I’m one of those people who stand in grocery stores and watch people read the labels on food,” said Ms. Day, 51, who will join Luvo part time in April and become CEO full time in September. The part time start was a concession to her husband, whom she had promised she would take a year off after leaving lululemon.

Luvo was founded by Steve Sidwell, the CEO of Devante Capital, a boutique investment bank based in British Columbia, who was looking to slim down after gaining 35 pounds. He was introduced to Ms. Day through a mutual friend. “Then I stalked her,” he said.

Ms. Day owns 15% of the company, making her the second largest investor behind Mr. Sidwell. Luvo has attracted other notable shareholders including Mr. Jeter, the New York Yankees shortstop, and, according to Mr. Sidwell, Ms. Garner. A representative for Ms. Garner didn’t return a call seeking comment.

Mr. Jeter is taking on the added role of brand development officer and will be involved in product development and the formation of strategic partnerships.

Another investor, according to Mr. Sidwell, is Dr. Mark Hyman, a New York Times best-selling author, who runs the Ultra Wellness Center in Lenox, Mass. Through books including the “The Blood Sugar Solution 10-Day Detox Diet,” Dr. Hyman advocates the importance of maintaining low insulin levels for health and weight loss. Dr. Hyman didn’t return a call seeking comment.

Mr. Sidwell said Luvo has raised all the money it needs for the foreseeable future from friends and family, though he declined to disclose the amount.

Ms. Day made a name for herself at Starbucks Corp., where she worked for two decades before joining lululemon in 2008. She presided over runaway growth at the Vancouver, British Columbia, maker of yoga gear, but also oversaw a debacle in which the company had to recall popular yoga pants because they were too see through. Lululemon is still grappling with the supply chain and damage to its reputation from that problem.

Luvo is also based in Vancouver, even though all of its revenue currently comes from the U.S.

Ms. Day said she hadn’t started looking for a new job when she was first contacted by Mr. Sidwell in September.

“The more I started thinking about what I wanted to do, the more I kept coming back to Steve and the story and thought it had a lot of legs,” she said.