"If we hope to escape self-destruction, then nuclear weapons should have no place in our collective conscience, and no role in our security," ElBaradei said at Saturday's awards ceremony in Oslo.
ElBaradei and the chairman of the Board of Governors of the IAEA, Yukiya Amano, received gold medals and Nobel diplomas at a ceremony in the Norwegian capital's City Hall.
The award was given for "their efforts to prevent nuclear energy from being used for military purposes".
The two men will share 10 million Swedish crowns ($1.25 million), which accompanies the award established by Swedish philanthropist Alfred Nobel.
ElBaradei has said his share of the prize will be donated to orphanages in his home country of Egypt.
The UN agency and ElBaradei received their award 60 years after the United States dropped two atomic bombs on Hiroshima and Nagasaki in Japan on 6 and 9 August 1945, the world's only nuclear attacks.
"At a time when the threat of nuclear arms is again increasing, the Norwegian Nobel Committee wishes to underline that this threat must be met through the broadest possible international cooperation," Chairman of the Nobel Committee Ole Mjoes said at the ceremony.
"In regions where conflicts have been left to fester for decades, countries continue to look for ways to offset their insecurities or project their power"
Mohamed ElBaradei, head of International Atomic Energy Agency
"This principle finds its clearest expression today in the work of the IAEA and its director general," he added.
'Threats without borders'
Speaking after receiving the award ElBaradei said the world should work to make nuclear weapons as universally condemnable as slavery or genocide.
The world, he said, has 27,000 nuclear warheads and that is "27,000 too many".
ElBaradei said the world faced "threats without borders" that could not be tackled by building walls, developing bigger weapons or dispatching troops, but only through multilateral cooperation.
"In regions where conflicts have been left to fester for decades, countries continue to look for ways to offset their insecurities or project their power," he said.
"In some cases, they may be tempted to seek their own weapons of mass destruction, like others who have preceded them," ElBaradei said.
"We must ensure - absolutely that no more countries acquire these deadly weapons," he said, adding, "We must see to it that nuclear-weapon states take concrete steps towards nuclear disarmament."
The IAEA was founded in 1957 to promote civilian use of nuclear energy and at the same time work to eliminate the proliferation of nuclear weapons.
The IAEA has been leading talks
over Iran's nuclear programme
"At a time when disarmament efforts appear deadlocked, when there is a danger that nuclear arms will spread both to states and to terrorist groups, and when nuclear power again appears to be playing an increasingly significant role, this work is of incalculable importance," Mjoes said.
The agency and its chief have most recently been instrumental in thorny nuclear negotiations with Iran, threatening to take the country before the UN Security Council for violating nuclear non-proliferation rules.
On Friday ElBaradei warned that the international community was losing patience with Iran over its nuclear programme, which Tehran insists is merely designed to meet domestic energy needs, but cautioned against using military action.
"I don't believe there is a military solution to the issue," he said.