The team have missed the last two rounds of the championship, in the United States and Brazil, due to ongoing financial issues and Kobayashi's regular 2014 team mate Marcus Ericsson severed ties with the squad last week.
"I am happy to be racing with the team in Abu Dhabi," said Kobayashi, whose partner for the Yas Marina event will be announced later in the week. "It hasn't been an easy last few weeks, so it will be nice to be back to in the car and work together with the Caterham F1 team members.
"I would like to thank the fans for supporting the team like they have. This team is working hard and never gives up. We deserve to be racing in Abu Dhabi and I am very glad we can race again thanks to the crowdfunding project.
"Now it is our turn to show what we can do - we will all try our best during the weekend ahead and hopefully we can end the season with a positive result for the future of this team."
Interim team principal Finbarr O'Connell added: "The team are delighted to have Kamui on board for the race weekend in Abu Dhabi. After the recent period of uncertainty for Caterham F1, the team are delighted, as part of (their) restructuring plan, to be able to showcase the cars again and what better way than with world-renowned drivers like Kamui?"
With the exception of Belgium, where he was replaced by former Le Mans winner Andre Lotterer, Kobayashi competed in every 2014 Grand Prix with Caterham prior to their US absence. The Japanese driver's best results have been 13th places in Malaysia and Monaco.