China's stake will not be more than 30% of the $100 million bank, a delegate told Reuters.
Asian countries are expected to own between 72 and 75% of the bank, Reuters said.
Each country representative will now take the proposals back to their governments for a final decision, a delegate told Reuters.
The meeting finalised the articles of agreement for the bank, and delegates discussed the environmental and social framework, and the draft procurement framework, the AIIB said in a statement.
The articles of agreement will be ready for signing by the end of June, and the AIIB will be operational by the end of the year, the AIIB said.
However, delegates who spoke to Reuters were less confident of the timetable: "It is uncertain if we can start from early next year," said one.
"China hopes that members will get such approvals by year-end and the operations start from the next year. But I wonder if it is possible, given domestic political situations in each country," the delegate told Reuters.
Fifty-seven countries have joined AIIB as its prospective founding members. The US and Japan have stayed out of the institution.
When the UK announced its plans to join the bank on 12 March, the US told the Financial Times that this was part of a trend of "constant accommodation" to China.