"I'm home... I only wish I could stay longer," he said to applause and cheers in a packed chamber.
On one of the longest foreign trips of his presidency, Biden became the fourth US president to address the parliament after John F Kennedy, Ronald Reagan and Bill Clinton.
A state banquet was planned for Thursday evening.
"Well mom, you said it would happen," he said looking skyward at the start of his speech, having met some of his late mother's distant relatives on Wednesday.
Biden began his trip on a more serious note in Northern Ireland, where on Wednesday he urged political leaders there to restore their power-sharing government with the promise of significant US investment.
But as soon as he crossed the border after that speech, he shifted gear to folksy anecdotes of his Irish relatives and photo ops with enthusiastic locals.
His great-great-grandfather Owen Finnegan left the Irish county of Louth for the United States in 1849.
On Friday, Biden is to meet relatives from another side of his family in County Mayo on the opposite coast of Ireland.
Providing plenty of images back home ahead of the 2024 election, Biden was pictured with a baby in the parliament, took selfies with reporters and got a sample of some Gaelic sports after meeting Prime Minister Leo Varadkar.
He acknowledged, however, that he was coming towards the end of his political career.
"I'm at the end of my career. Not the beginning. The only thing I bring to this career - and you can see, how old I am - is a little bit of wisdom."
Biden quipped he did not want to go back to the US while meeting fellow octogenarian, Irish President Michael D Higgins.
Higgins previously hosted then-vice president Biden at his residence in Dublin's Phoenix Park in 2016, and again in 2017.
Biden said he quoted the Irish proverb that "your feet will bring you where your heart is" when signing the visitors' book, and wrote that it was an honour to return to the home of his ancestors to celebrate all that binds Ireland and the US.
Higgins, who shares Biden's passion for Irish poems and has written many himself, presented the president with a vinyl copy of Patrick Kavanagh's poetry, which includes some of the poet's work read by U2 singer Bono, actor Liam Neeson and Higgins.
Known for frequently quoting Irish poet Seamus Heaney, Biden referenced the late Nobel Prize-winner again in parliament, this time with Heaney's wife Marie in attendance.
Biden, accompanied for some of his Dublin engagement by his son Hunter, sister Valerie and US Secretary of State Antony Blinken, will be guest of honour at a banquet at St Patrick's Hall in Dublin Castle on Thursday evening.
