The AIIB's board of governors adopted resolutions approving the three applicants to join the bank at the second annual meeting, which kicked off earlier in the day in South Korea's southern resort island of Jeju.
The first meeting was held in Beijing last year.
The approved applicants included one regional prospective member of Tonga and two non-regional members of Argentina and Madagascar.
"Well-integrated infrastructure and enhanced connectivity between Asia and the rest of the world has far-reaching benefits for the global economy," said AIIB President Jin Liqun.
Tonga was well known as the friendly islands in the South Pacific, while Argentina and Madagascar are important economies in South America and Africa each, said Jin.
The AIIB chief expressed his anticipation of the role the three new members will play once they fully join the bank.
The three prospective members will officially join the AIIB once they complete the required domestic processes and deposit the first installment of capital with the bank.
The shares allocated to the new prospective members come from the bank's existing pool of unallocated shares.
"Since launching only 18 months ago, the bank has welcomed 23 new members from around the world," said Sir Danny Alexander, vice-president and corporate secretary at the AIIB.
The vice-chief said interest in the AIIB remained high and that the bank's door remained open to new members that will be joining later this year.
Officially launched in January 2016, the Beijing-based AIIB is a multilateral development bank initiated by China and supported by a wide range of countries and regions, which will provide financing for infrastructure improvement in Asia.
The international infrastructure bank owned about $100 billion of subscribed capital, including some $20 billion in paid-in capital.
This year's annual meeting brought together about 2,000 participants, including delegations of both founding members and new members, international organizations and academia as well as businessmen, financiers and journalists.
The attendees included over 20 finance ministers of the approved AIIB members, according to South Korea's finance ministry.
The second annual meeting was held under the theme of "Sustainable Infrastructure," seeking strategic directions of the international infrastructure bank and making major decisions on the bank's management.
