The ceremony was held at the Great Hall of the People in Beijing on Monday with Iran's Minister of Economic Affairs and Finance Ali Tayyebnia in attendance.
Representatives from 50 countries signed the articles that determine each member's share and the bank's initial capital.
China's finance ministry said seven other countries that had applied to join did not sign the agreement because they did not yet have domestic approval.
China is the largest shareholder in the bank, with a stake of 30.34 per cent.
The UK, Germany, Australia and South Korea are among the founding members. Japan and the US, which oppose the AIIB, are the most prominent countries not to join, according to media reports.
The AIIB was created in October by 21 countries, led by China, to fund Asian energy, transport and infrastructure projects.