The British supermarket giant, the world's third largest retailer, has been looking to dispose of its loss-making US food chain for some time.
Around 4,000 of Fresh & Easy's 5,000 employees are to transfer to the new business as part of the deal.
Tesco said in a statement that this is an "orderly and efficient exit from the US market".
Under the terms of the deal, Tesco will loan the new business around Â£80m.
Fresh & Easy, which operates 200 stores across California, Nevada and Arizona, has lost money since opening in 2007.
Tesco did not specify which stores are being transferred to Yucaipa, but it is understood the remaining 50 shops will be closed.
It will cost Tesco Â£150m to dispose of the Fresh & Easy brand, but part of that is a loan which may be paid back.
Also, if Yucaipa is sucessful and the business becomes profitable, Tesco has the option to buy a stake.
Yucaipa is a Los Angeles based private equity company focused on supermaket and restaurant businesses and is run by billionaire investor Ron Burkle.
In April of this year, Tesco reported its first fall in annual profits for 20 years.

Jamie Peacock, Kevin Sinfield and Kylie Leuluai ended their rugby league playing careers with the 22-20 win over Wigan Warriors at Old Trafford, which completed Leeds' domestic treble.
"I do believe it gave us an edge," McDermott told BBC Sport.
"For Kylie, JP and Sinfield to go out on that note, that is fitting as well."
Speaking after the win, which attracted a Grand Final record crowd of 73,512, McDermott added: "Everybody wanted to tip in, that was the difference."
For Sinfield, the longest serving of the trio, it was his final game in the 13-man code before switching to rugby union's Yorkshire Carnegie, starting next month.
The Leeds and former England captain admitted it was an emotion-charged send-off.
"It was joy," Sinfield said when asked what it felt like to finish as a treble-winning captain.
"Thankfully the guys jumped on me and hid a few of the tears. They were tears of joy. It was an unbelievable way to finish."
The defeat marked the end of Wigan full-back Matty Bowen's career, while winger Joe Burgess also said farewell as he joins Sydney Roosters.
Bowen, who scored a brilliant solo try to put Wigan 18-16 ahead in the second half, said it was a "surreal" occasion, having become a father for the third time just before midnight on the eve of the game.
Daughter Tatum was in the stands with the rest of Bowen's family, 16 hours after being born.
"It's been a busy two days at the hospital... we've had a beautiful little girl," said Bowen, who will take up a role with former club and newly crowned NRL champions North Queensland Cowboys as part of their community coaching team.
"She is healthy, that's the main thing. We haven't told anyone, for nine months nobody knew. I surprised my mum two weeks ago.
"I just want to relax now and enjoy time with the family and watch them grow."

The site - which is owned by Google - is launching a competition for teenagers to create an experiment that could be carried out in space.
Two winning ideas will be tested by the crew of the International Space Station.
Google chairman Eric Schmidt recently criticised science and technology education in the UK.
Delivering the annual McTaggart lecture in Edinburgh, Mr Schmidt said the country needed to reignite children's passion for subjects such as engineering and maths.
In addition to having their experiment run in space, the winners will get to experience weightlessness on a zero-g airplane flight, and have the option to either undergo astronaut training in Russia, or to watch the rocket launch in Japan which takes their idea into space.
When the experiments are eventually run, the results will be streamed live on YouTube.
The competition is divided into two age groups. 14-16 years, and 17-18 years.
Alongside Prof Hawking, the judging panel consists of former Astronauts Leland Melvin, Frank De Winne, Akihiko Hoshide and noted "space tourist" Guy LalibertÃ©.
Tesco has agreed to sell 150 of its Fresh & Easy stores to the investment company Yucaipa Companies.
[NEXT_CONCEPT]
Leeds Rhinos were given a decisive boost for the Grand Final by the emotion surrounding their departing trio, says head coach Brian McDermott.
[NEXT_CONCEPT]
YouTube has enlisted the help of Prof Stephen Hawking in the hunt for budding young scientists.