Cesare Prandelli's side have agreed to come to London as part of their final preparations for the World Cup in Brazil, where they face England in the group stage.
Prandelli's team will return to Italy after the match for their final warm-up against Luxemburg four days later.
The Italians drew 2-2 with Nigeria in a Craven Cottage friendly in November and face England on June 14 in their tournament opener before also playing Costa Rica and Uruguay in Group D.
Italy will be Ireland's fifth opponents since the management team of O'Neill and Roy Keane took over from Giovanni Trapattoni.
O'Neill has won one, drawn one and lost one of his three games as boss, and the Italy game comes six days after a home friendly against Turkey.
Ireland have played the four-time World Cup-winners 13 times, winning two and drawing two.