"As Vice President, JD will continue to fight for our Constitution, stand with our Troops, and will do everything he can to help me MAKE AMERICA GREAT AGAIN," Trump wrote on his Truth Social platform.
Trump made the announcement at the start of the Republican National Convention, two days after he survived an assassination attempt.
The selection of James David Vance, author of the bestselling memoir Hillbilly Elegy, could increase the odds of Trump supporters turning out for the November 5 election as the Ohio native is deeply popular with the Republican candidate's base.
Earlier on Monday, Trump was handed a major legal victory when a federal judge dismissed one of his criminal prosecutions.
US District Court Judge Aileen Cannon ruled that the prosecutor who charged Trump with mishandling classified documents was unlawfully appointed to his role.
Trump is due to formally accept the party's nomination on Thursday to challenge Democratic President Joe Biden in the November 5 election.
Trump, 78, and Biden, 81, are locked in what opinion polls suggest is a tight election rematch.
After the assassination attempt, Trump said he is revising his acceptance speech to emphasise national unity, rather than highlight his differences with Biden.
"This is a chance to bring the whole country, even the whole world, together. The speech will be a lot different, a lot different than it would've been two days ago," Trump told the Washington Examiner.Â
The would-be assassin's bullet clipped Trump's right ear but did no major harm.
The shooting on Saturday whipsawed discussion around the presidential campaign, which had been focused on whether Biden should drop out due to concerns about his age and acuity following a halting June 27 debate performance.
Nearly two dozen of Biden's fellow Democrats in Congress have called on him to end his re-election bid and allow the party to pick another standard bearer.
with AP
