Trump promises a safer America as he becomes the official Republican candidate
"The crime and violence that today afflicts our nation will soon come to an end," he said in Cleveland.
Painting a bleak picture of the state of the country, he said his presidency would usher in a new era putting America and ordinary people first.
His speech comes a day after Senator Ted Cruz failed to back him.
The senator, who was his bitter rival during the primary contests, was booed off the stage by Mr Trump's supporters.
Other senior Republicans like former presidents George HW Bush and George W Bush have stayed away from the convention in protest at the coronation of a nominee they so vehemently oppose.
But Mr Trump, a New York businessman who was written off when he launched his campaign a year ago, hoped his speech would allay these tensions and unite the party.
Speaking for well over an hour, he said the security of the country was under threat from Islamic radicals, undocumented immigrants and trade deals that fail American workers.
"We will lead our country back to safety, prosperity, and peace. We will be a country of generosity and warmth. But we will also be a country of law and order," he said.
Addressing the "forgotten Americans" who work hard but no longer have a a voice, he said: "I am your voice."
He attacked his Democratic rival Hillary Clinton at every opportunity, blaming the former secretary of state for "death, destruction and weakness".
In a speech he described as a plan to "put America first", Mr Trump said:
He would build "a great border wall" to stop illegal immigration, gangs and drugs
Mrs Clinton is proposing mass amnesty, mass immigration, and mass lawlessness.
Decades of immigration have produced lower wages for African Americans and Latinos
President Obama has failed US inner cities on education, jobs and crime
Nearly 180,000 illegal immigrants with criminal records are "roaming free" to threaten citizens trade deals that have "destroyed our middle class" will come to an end "Americanism, not globalism" would be the tenet of foreign policy.
He was introduced in glowing terms by his daughter Ivanka, who said her father valued women workers and he would make quality childcare affordable.
Not long into his speech, he deflected crowd chants of "Lock her up!" by saying he would beat Hillary Clinton in November.
In a departure from Republican orthodoxy, Mr Trump took up the theme of acceptance of LGBT rights, framing it in terms of American values.
"I will do everything in my power to protect our LGBTQ citizens from the violence ... of the hateful foreign ideology," he said to some cheers from the crowd.
"As a Republican it is so nice to hear you cheering for what I just said," he added.
In a key moment earlier in the night, Silicon Valley mogul Peter Thiel told the convention he was proud to be gay.
The chairman of the Hillary for America campaign, John Podesta, attacked Mr Trump's speech as divisive.
"Tonight, Donald Trump painted a dark picture of an America in decline. And his answer - more fear, more division, more anger, more hate - was yet another reminder that he is temperamentally unfit and totally unqualified to be president."
Texas Senator Mr Cruz caused a storm on Wednesday night when he pointedly refused to back the nominee.
The moment sparked outrage among crowd members, who began booing Mr Cruz and chanting, "Endorse Trump!" and "We Want Trump!" before he finished his remarks.
He later defended his decision, saying he would not be a "servile puppy" to someone who had attacked his wife and father.
Mr Trump has previously suggested that Mr Cruz's father was involved in the assassination of John F Kennedy and criticised the appearance of his wife, Heidi.
Mr Trump's nomination has been a primary source of conflict within the party, with some like Mr Cruz questioning his conservative principles.
Others like former nominee Mitt Romney are concerned about his strident tone and extreme stance on immigration.