The House Speaker, Paul Ryan, urged delegates to unite behind Mr. Trump, a day after splits in the party were evident as the convention opened.
The Trump campaign also faces accusations a speech by Mr. Trump’s wife Melania on Monday was plagiarised.
Tuesday’s speakers focused almost exclusively on attacking Hillary Clinton, the likely Democratic nominee.
New Jersey Governor Chris Christie, a former prosecutor, held a mock trial for Mrs. Clinton as the crowd chanted “lock her up”.
Mr. Christie and others criticised Mrs. Clinton’s use of a private email account while she was serving as secretary of state.
An FBI investigation said she was “extremely careless” but found her actions didn’t warrant criminal prosecution. However, Mr. Christie and the crowd disagreed as Mr. Christie repeatedly yelled “guilty”.
He said she has “selfish, awful judgement” and was to blame for various foreign policy problems in Libya, Syria and elsewhere.
Mr. Trump is expected to accept the nomination on Thursday.
His children played a prominent role on Tuesday, standing with the New York delegation as he was declared winner and delivering remarks.
The result hasn’t really been in doubt for months, but now it’s a reality. The Republican Party’s nomination for president of the United States is Donald Trump’s to accept when he takes the stage on Thursday night.
Thanks to a bit of procedural manoeuvring, it was New York that gave him the winning margin in the state-by-state roll call vote. His oldest son, Donald Trump Jr, voice wavering with emotion, made it official.
“Congratulations, Dad, we love you,” he said. -BBC