Australia has also said that it will reconsider its position on joining the $50 billion AIIB, which is seen as a potential rival to the World Bank, the Financial Times said.
The AIIB was launched in Beijing last year to boost investment in infrastructure in Asia. Much of the initial finding came from China, but founding members included 26 countries, mostly from Asia and the Middle East, Deutsche Welle said.
President of the European Parliament Martin Schulz welcomed the participation of EU countries in the bank, and said: "I think participation is good; the more countries take part, the better," Deutsche Welle said.
The US has attempted to discourage western countries from joining the AIIB, saying that they will have more power in working jointly from outside the bank, pushing for higher lending standards, the Financial Times said.
The AIIB has become an focal point in the struggle between the US and China over who will influence economic and trade rules in Asia. When the UK announced its plans to join the bank, the US told the Financial Times that this was part of a trend of "constant accommodation" to China.
However, infrastructure expert Richard Laudy of Pinsent Masons, the law firm behind Out-Law.com, said at the time of the UK announcement that that the move to become a founding member of the bank could create "massive" trade and investment opportunities for UK firms in the Far East.
The UK could potentially play a significant role in Asian infrastructure investment over the next decade. At the same time, UK infrastructure was a "highly attractive" market for Chinese investors, he said.
China foreign ministry spokesman Hong Lei said that "the AIIB is an open and inclusive multilateral organisation. We welcome interested parties to join it," Chinese state-owned news agency Xinhua said.
China is ready to work with all sides to make the AIIB a "reciprocal and efficient platform", he told Xinhua.
The bank is expected to be formally established by the end of this year, Xinhua said, and the deadline to join is 31 March.