The first box of documents was handed over in the demilitarised border zone along the Iraqi-Kuwaiti frontier, under the supervision of the United Nations.
An Arab League team is also taking part in the process.
Five trucks of official papers have been driven down from Baghdad.
They are said to include the files of the Kuwaiti foreign ministry, the national security department and the interior ministry, and correspondence relating to Kuwaiti-American relations.
Iraq says the handover is in keeping with promises made at the Arab League summit in Beirut, last March.
A UN official, speaking on condition of anonymity, said the Kuwaitis were now inspecting the boxes before officially accepting them.
"Every day a few boxes will be unloaded and checked by the Kuwaitis. It'll be a long procedure."
UN resolution
The return of the archives was demanded in a UN resolution - one of those which the US is demanding Iraq obeys or face military action.
Kuwaiti Foreign Minister Sheikh Sabah al-Ahmad al-Sabah said he hoped the return of the documents would herald progress on prisoners who have not been seen since the Gulf War.
"Even though it [return of archives] is important, there is something more important to us, which is the issue of the PoWs," he said.
"Everyone in Kuwait is waiting for the PoWs."
Kuwait maintains that 605 of its and other countries' nationals disappeared during the Iraqi occupation of the emirate, and claims they are still being held in Iraq.
Iraq has admitted taking prisoners but said it lost track of them during a Shia Muslim uprising in southern Iraq following its retreat from Kuwait.
Baghdad claims 1,142 of its own nationals have been missing since the Gulf conflict.