After several rounds of voting on Thursday, the candidate scored the required two-thirds majority from the 35-nation governing board, defeating Abdul Samad Minty, his South African rival.
"This afternoon I have received the support from 23 countries, which is the necessary number of votes to be selected as the next director-general of the IAEA," Amano said after the vote.
"I am very pleased for this support."
Amano had earlier pledged to do his "utmost to enhance the welfare of human beings and ensure sustainable development through the peaceful use of nuclear energy" if elected.
"Also, as a national coming from Japan, I'll do my utmost to prevent the spread of nuclear weapons," he said.
"In order to do that, solidarity of all the member states countries from North, from South, from East and West is absolutely necessary."
Broad consensus
Amano had the backing of several industrialised nations on the agency's governing board.
But other countries had voiced concern about his ability to tackle rising threats to the global nuclear non-proliferation and his support of a tough approach to dealing with Iran's disputed nuclear programme.
Many nations had wanted an IAEA leader with broad consensus backing to tackle threats to the global nuclear non-proliferation regime.
Earlier, an EU diplomat said, Russia had told other board members that it would be "unacceptable" if Amano was elected by only the minimum winning margin.
Such an outcome would harden a North-South split undermining the next IAEA chief's authority, he said.
El Baradei, an Egyptian diplomat, has been in the job for 12 years and served three terms.
Amano will assume the highly sensitive nuclear dossiers of Syria, Iran and North Korea and will also have to persuade IAEA member countries to contribute more money to its budget.
El Baradei, who won the the Nobel Peace Prize in 2005 for his work at the IAEA, has often been criticised as being too outspoken and has also been accused of politicising the agency.