A joint statement said a deal had been agreed with the government, which had allocated £900m for the authority to spend over 30 years.
Portsmouth leader Donna Jones said the official announcement was expected within weeks.
But she said plans to create a joint mayor would be postponed until May 2018 at the earliest.
Southampton City Council said neighbouring district authorities had now been excluded from the proposed Solent Combined Authority, because of opposition from Hampshire County Council.
The leader of Labour-controlled Southampton, Simon Letts, said: "We are disappointed that despite our best efforts to persuade them, Hampshire County Council will not sign up and support our bid to double the size of the regional economy."
But Hampshire's Conservative leader Roy Perry said: "It's not correct to say that Hampshire County Council has opposed any proposed deal.
"We have simply confirmed that we are not prepared to join any arrangements unless and until the residents of Hampshire show their support."
Mr Perry said his authority would hold a full public consultation.
Isle of Wight Council leader Jonathan Bacon, an Independent, said: "The Island has recently been told by the Secretary of State... that no extra money will be found for the Isle of Wight to meet its current financial difficulties.
"It is, therefore, important that we... obtain a share in the pot of £900 million that has currently been set aside for a local devolution deal."
The joint statement said as a result of the combined authority, "more people would get jobs, businesses would prosper, and the whole of South Hampshire and the Isle of Wight would become better off".
Ms Jones, who leads a Conservative administration at Portsmouth City Council, said that much of the £900m would initially be spent on transport projects, including a new light rail system between Southampton and Fareham.
She said the new authority could be up and running by March, following legislation in parliament.
The three councils would leave the current system of government funding in exchange for keeping business rates, of about £400m a year, on top of the £900m agreed with the government.
Southampton, Portsmouth and Isle of Wight councils have announced plans to create a combined authority.