The council lifted the threat of sanctions linked to the search for Kuwaitis and property missing since the invasion by Saddam's forces.
Iraq's Foreign Minister Hoshyar Zebari called the unanimous vote a "landmark" in efforts by Iraq and Kuwait to heal the wounds caused by the invasion, which was ended by an international coalition in 1991.
The vote is a major boost to Iraq's efforts to restore its international standing after the toppling of the dictator in 2003 by a US-led invasion.
They had previously been dealt with under Chapter VII of the charter, which allows for sanctions and military intervention to enforce council demands.
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The UN still has an arms embargo against Iraq under Chapter VII, and the sanctions threat remains for Iraq's payment of war compensation to Kuwait.
Iraq was ordered to pay just over USD 52 billion to its neighbour. Iraq says it still owes about USD 11 billion and that the debt will be fully paid in 2015.
In a recent report that recommended the easing of sanctions, UN leader Ban Ki-moon said that both governments had shown "statesmanship and respect" in their recent dealings.