Southampton, Portsmouth and Isle of Wight councils want to create the authority to take on services currently managed by central government.
A public consultation on the plans begins on Friday.
Under the deal, the councils would leave the current system of government funding in exchange for keeping business rates of about Â£210m a year.
They would also secure Â£900m from government to spend over 30 years on infrastructure.
Each of the councils would continue as separate entities and retain their existing powers but they would also be equal members on a board, led by an elected mayor.
Southampton City Council leader Simon Letts said: "This deal will enable us to be in control of our own destiny and will enable us to secure new powers and funding from government."
A consultation will run until 18 September.
Three councils have approved draft plans to create a combined authority for the Solent area.