Welby, the leader of the world's 80 million Anglicans, will also visit the tombs of St Peter and John Paul II at St Peter's Basilica, the Vatican said in a statement today, adding that he will be accompanied by his wife Caroline.
He will also meet Swiss cardinal Kurt Koch, head of the Vatican's Council for Christian Unity.
Francis's predecessor Benedict XVI enjoyed generally good relations with his Anglican counterpart Rowan Williams, though relations were strained by a Vatican move to make it easier for disaffected Anglicans to switch to the generally more conservative Catholic Church.
Anglicans are themselves divided between liberals and conservatives -- principally in Africa -- on issues such as gay rights and women's ordination.
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The two churches have been divided since King Henry VIII broke with Rome and set himself up as the head of the new Church of England in 1534.
Benedict made a single state visit to Britain in 2010.
Welby missed the March inauguration of Pope Francis as he was on a pilgrimage.