"She accepted the invitation and will discuss a visit there at a mutually convenient time," Aye Aye Soe, a Ministry of Foreign Affairs official, told AFP.
The invitation reinforces Suu Kyi's primacy on the international stage as the real head of a government she is technically barred from leading.
Despite winning a landslide in last November's elections, an event that brought to an end decades of brutal military rule, Suu Kyi is banned from being president by a junta-era constitution.
It is not clear when the visit will take place but it is expected to occur before Obama leaves office as American voters head to the polls in November.
"President Obama has six months of his term left and they would like to maintain good relations between our two countries," Aye Aye Soe said.
Ben Rhodes, Obama's Deputy National Security Advisor for Strategic Communications, delivered the invitation yesterday during a visit to the capital Naypyidaw.
President Obama also met Suu Kyi during a visit to Myanmar in 2014 in which he criticised the ban on Suu Kyi taking the presidency.
Myanmar's peaceful transition from military to civilian rule has been hailed in a world where such transitions seem rare.
But the military, who spent decades brutalising the population and enriching themselves, remain enormously influential.
Officers are still guaranteed a quarter of legislative seats, giving them a veto on constitutional change, while the military retains control of the crucial home, border and defence ministries.
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