Iran would then - as per the terms of the agreement- use the nuclear fuel rods for its Tehran medical research reactor.
The move aims to ease Western concerns over Iran's nuclear programme, and stave off a possible new round of sanctions by the United Nations.
Mahmoud Ahmadinejad, the Iranian president, signed the deal on Monday following a breakfast with his Brazilian counterpart Luiz Inacio Lula da Silva and Recep Tayyip Erdogan, the Turkish prime minister.
After the deal's announcement, Ahmadinejad called on the permanent members of the UN Security Council, as well as Germany, to relaunch dialogue over Iran's nuclear programe.
"It is time for the 5+1 countries to enter talks with Iran based on honesty, justice and mutual respect," he said.
It was not immediately clear whether the terms of the deal would fully satisfy the demands made by the Security Council members.
Ahmet Davutoglu, Turkey's foreign minister, first announced a breakthrough in the talks late on Sunday, after what he said was "almost 18 hours of negotiations".
Speaking after Monday's formal signing, Davutoglu said there was no longer any justification for more UN sanctions on Iran.
"The swap deal, signed by Iran today, shows that Tehran wants to open a constructive path ... There is no more ground for new sanctions and pressures," he said.
The plan calls for Turkey to be the conduit for the fuel swap, but as Iran's neighbour doesn't possess the technology to enrich uranium, it would instead hold the material as a guarantee.
John Large, an independent nuclear consultant, said that guarantee may not be enough reassurance for the international community to agree to hand over fuel rods to Iran.
"Turkey has no facilities whatsoever. It is not a nuclear country, so it has no enrichment facilities, and of course, it doesn't really have any storage facilities," he said.
"This deal has to be guaranteed in terms of storage security and transportation security."
The IAEA, the UN's nuclear watchdog group, would also insist on carrying out various tests on the transferred material in order "to make sure that it is low enriched uranium of the quality required for exchange," Large said.
Manouchehr Mottaki, the Iranian foreign minister, said in the event the deal is not implemented, Iran's uranium would have to be returned straight away.
"Based on the agreement signed this morning, if the swap does not take place, then Turkey will be obliged to send back our dispatched uranium immediately and unconditionally," he said.
Iran has also not agreed to halt its low-level uranium enrichment, and confirmed plans to continue.
Lula had flown in to broker the deal, in what was called a last-ditch mediation attemptbefore new sanctions were imposed.
The US and Russia had warned that the chances of success were weak but on Sunday, Erdogan postponed a trip to Azerbaijan to join the negotiations.
Iran has previously been reluctant to allow its stockpile of uranium to leave the country before receiving the nuclear fuel, saying that the exchange must take place simultaneously inside the country.
Last week, however, Mohsen Shaterzadeh, Iran's ambassador to Brazil, said that an exchange in another country might be acceptable.
Brazil and Turkey, both non-permanent members of the UN Security Council, have resisted US-led efforts to push through new sanctions against Iran over its failure to accept repeated ultimatums to stop uranium enrichment activity.
The US and its allies say that Iran wants highly enriched uranium to make an atomic weapon, but Tehran says its programme is simply designed to meet its civilian energy needs.
Lula has in the past defended Iran's nuclear activities, saying Tehran has the right to atomic energy, and has repeatedly said sanctions would be counter-productive and ineffective.