He will now face Hillary Clinton in November's US election
Trump gained 1,725 delegates, with Texas senator Ted Cruz on 475, Ohio governor John Kasich on 129 and Florida senator Marco Rubio on 113.
In a video message, Trump said that winning the nomination was something he would "never forget" and said he would "win the presidency and bring real change and leadership back to Washington".
The nomination process was opened by Alabama senator Jeff Sessions who declared billionaire Trump to be "a warrior and a winner".
New York Representative Chris Collins seconded the nomination, saying that Trump would defeat terrorism and make the US safe again.
Trump's former campaign manager Corey Lewandowski announced that his home state of New Hampshire was also casting its votes for "my friend and the next president of the United States, Donald J Trump".
Lewandowski was fired by the Trump campaign last month but has continued to voice his support for his old boss in his new job as a commentator on CNN.
The final announcement was made by Trump's son Donald Jr, who told delegates that New York was casting 89 votes for Trump and six for Ohio governor John Kasich.
He added: "It's my honor to be able to throw Donald Trump over the top in the delegation count tonight.
"Congratulations, dad, we love you."
His words were greeted with thunderous applause from convention delegates at the Quicken Loans Arena in Cleveland, Ohio.
Trump, 70, had earlier tweeted about his excitement as the roll call began.
The ROLL CALL is beginning at the Republican National Convention. Very exciting!— Donald J. Trump (@realDonaldTrump) July 19, 2016
He is expected to formally accept the nomination in a speech on Thursday, and will then face Democrat Hillary Clinton in November's presidential election.
Republicans also placed Indiana governor Mike Pence's name on the nomination for vice president.
On the first day of the convention, Republicans against Donald Trump were thwarted in a last-ditch bid to vote against the tycoon.
The Trump campaign had fought back by circulating a form allowing people to remove their names from the petitions.
There was also controversy after parts of a speech by Trump's wife Melania were revealed to match almost word-for-word one given by current First Lady Michelle Obama in 2008. Trump adviser Paul Manafort said the matter had been "totally blown out of proportion".