The group, formed in 2007, is made up of twelve global leaders who try "to promote peace, justice and human rights," according to their website.
The group sees "recent positive developments as a historic and strategic opportunity to end decades of animosity between Iran and the international community," the statement published today said.
But it added "trust will only be built slowly, through continued goodwill and reciprocal action."
During the visit, the Elders "will exchange ideas with the Iranian leadership about peaceful ways of addressing conflict".
President Hassan Rouhani won last year's presidential elections with promises of a more diplomatic approach to the West.
Iran and major world powers clinched a historic nuclear deal in November, when Tehran agreed to curb parts of its nuclear programme for six months in exchange for modest sanctions relief and a promise by Western powers not to impose new sanctions.