The countries are expected to establish the Beijing-based AIIB formally by the end of next year with authorised capital of 100 billion dollars, state media said.
Following the singing of a memorandum of understanding on forming the bank, Chinese President Xi Jinping met representatives from the other countries involved, including India, Pakistan, Bangladesh, Malaysia, the Philippines and Thailand.
The United States opposed the formation of the bank, but the Asian Development Bank gave a cautious welcome to Friday's agreement and said it would "consider appropriate collaboration" with the AIIB.
The 21 singatories of Friday's memorandum are Bangladesh, Brunei, Cambodia, China, India, Kazakhstan, Kuwait, Laos, Malaysia, Mongolia, Myanmar, Nepal, Oman, Pakistan, the Philippines, Qatar, Singapore, Sri Lanka, Thailand, Uzbekistan and Vietnam.