In his speech in Dundalk, Mr Biden said his ancestors left Ireland at about the same time as former US President Barack Obama’s great-great-great-grandfather Falmouth Kearney, who was from Moneygall in County Offaly.
“They would never have dreamed that their grandsons would have been presidents of the United States,” he said.
Mr Biden was given a tour of Carlingford Castle alongside the Tánaiste (Irish Deputy Prime Minister) Micheál Martin.
Asked about his feelings on the visit, the president replied: “It’s wonderful. It feels like I’m coming home.”
Commenting on the wet weather, he added: “It’s fine – it’s Ireland.”