The Inca nation is one of the 8 non-regional countries joining the multilateral financial institution, along with Belgium, Canada, Ethiopia, Hungary, Ireland, Sudan and Venezuela.
AIIB has also formally approved regional applicants Afghanistan, Armenia, Fiji, Hong Kong, China and Timor Leste.
Approval resolutions thus push AIIB membership —initially at 57— to 70.
"The interest in joining AIIB from around the world affirms the rapid progress we have made to establish the Bank as an international institution," said at that time AIIB President Jin Liqun.
The 13 prospective members will officially join AIIB once they complete the required domestic processes and deposit the first installment of capital with the Bank.
"I am very proud that AIIB now has members from almost every continent," he added.
Shares allocated to the new prospective members come from the Bank's existing pool of unallocated shares.
Peru applied to join the China-backed institution last year in an attempt to gain access to low-cost long-term financing for major infrastructure works.
AIIB is a new multilateral financial institution founded to bring countries together to address the daunting infrastructure needs across Asia.
Headquartered in Beijing, AIIB's mission is to improve economic and social development in Asia by investing in high quality, financially viable and environmentally friendly infrastructure projects.