Accepting the Republican nomination in a speech in Cleveland, Ohio, he said: “The crime and violence that today afflicts our nation will soon come to an end.”
The businessman’s nomination has been clouded by the refusal of major party figures including Senator Ted Cruz to endorse him.
Mr Cruz, who was his bitter rival during the primary contests, was booed off the stage by Trump supporters.
Other Trump opponents such as members of the Bush family stayed away from the convention altogether.
Mr Trump said he hoped his speech would ease tensions and unite the party.
His forceful promises to be the champion of disaffected Americans closed out his convention on a high note for the party, not a moment too soon after shows of disharmony before Thursday night’s closer.
Speaking to “the forgotten men and women of our country,” the people who “work hard but no longer have a voice,” he declared: “I am your voice.”
With that, he summed up both the paradox and the power of his campaign – a billionaire who made common cause with struggling Americans alienated from the system, or at least a portion of them.
He pledged as president to restore a sense of public safety, strictly curb immigration and save the nation from Democrat candidate Hillary Clinton’s record of “death, destruction, terrorism and weakness”.
“I have joined the political arena so that the powerful can no longer beat up on people that cannot defend themselves,” Mr Trump said.
Mrs Clinton was expected to announce her running mate either at a rally in Florida last night or today in Miami.
Tim Kaine, 58, appeared to be the favourite for her choice, according to two Democrats, who both said that Mrs Clinton has not made a decision and could change direction.
In Cleveland, Mr Trump’s acceptance of the Republican nomination capped his improbable takeover of a party that plunges into the general election united in opposition to Mrs Clinton but still torn over Mr Trump.
Underscoring his unorthodox candidacy, Mr Trump reasserted the hard-line immigration policies that fired up conservatives in the primary but broke with many in his party by promising protections for gays and lesbians.
Mr Trump’s speech was strikingly dark for a celebratory event and almost entirely lacking in policy details. He also showed few flashes of humour or even a smile.
“This is the legacy of Hillary Clinton: death, destruction, terrorism and weakness,” he said. “But Hillary Clinton’s legacy does not have to be America’s legacy.”
In a direct appeal to Americans shaken by a summer of violence at home and abroad, Mr Trump promised that “safety will be restored”.