The agreement will allow the institutions to finance development projects together, thetwo institutions said in a joint statement.
The banks are discussing "nearly one dozen" co-financed projects in sectors including transport, water and energy in Central Asia, South Asia and East Asia, they said.
The AIIB expects to approve about $1.2 billion in financing in 2016, with World Bank joint projects accounting for "a sizable share" of these, it said.
Under the agreement, the World Bank will prepare and supervise the co-financed projects "in accordance with its policies and procedures in areas like procurement, environment and social safeguards", it said.
The World Bank Group invested $18.8 billion in infrastructure in the fiscal year to June 2015. It will leverage further private finance through new partnerships, such as the Global Infrastructure Facility, and the growing portfolios of the International Finance Corporation and the Multilateral Investment Guarantee Agency, it said.
The AIIB is working with other multilateral and bilateral development institutions to promote regional cooperation in addressing development challenges, the statement said.
Project finance expert John Yeap of Pinsent Masons, the law firm behind Out-Law.com said: "The demand for financing of essential infrastructure across Asia and wider afield is immense. Co-financing by the World Bank and the AIIB is a collaborative step that underlines what can be delivered through aligning the objectives of development agencies with the aspirations of developing nations struggling to finance infrastructure. Such institutions have an essential role to play in bridging the funding gap, and co-financing is one step towards bringing consistency in lending criteria across the institutions."
The Chinese-led AIIB was announced in Beijing in 2014, with the aim of boosting investment in infrastructure in Asia and was established formally by the 57 member countries signing the Articles of Agreement in June 2015.
It is expected to have initial capital of close to US$100 billion to invest in infrastructure projects and will be financed by individual country contributions proportionate to their economic size.
The Financial Times reported last month that the AIIB plans to offer joint loans with the Japanese-led Asian Development Bank (ADB).
The two banks are also working on procedures to ensure that loans include safeguards in labour, environmental and anti-corruption rules, ADB president Takehiko Nakao told the newspaper.
People have been keen to depict the two banks and their presidents as rivals, "but actually we are friends, and ADB and AIIB can be partners", Nakao said.
"We’re already identifying projects for the first batch of AIIB loans. One of them should be co-financing between AIIB and ADB," he said.