The firm also announced the formation of a joint venture between the three companies to sell refined oil products on international markets.
The concession will be operated by Eni, and will be fully-owned by the Italian company and the government-owned Thai producer.
Descalzi said Eni's "epochal" announcement on how it planned to reach its goal would be made by the end of the year, adding that no oil company as yet had laid out binding plans for a net zero carbon footprint.
The new company, named Vaar Energi and led by Point Resources' Vice President Kristin F. Kragseth, will be one of the largest players on the Norwegian continental shelf with a portfolio of 17 producing oil and gas fields.
Once the contracts have been signed, Exxon plans to drill two wells and Eni at least one next year.
Eni CEO Claudio Descalzi, his predecessor Paolo Scaroni and several officials from Eni and Shell are among those facing the judge.