The declaration, with wife Melania finally appearing alongside him, came as rival Joe Biden clung on to hopes of staying on in the White House.
Trump told delegates at the Republican National Convention that the bullet "came within a quarter of an inch of taking my life".
He told the audience: "Just a few short days ago my journey with you nearly ended."
The ex-president was shot by 20-year-old Thomas Matthew Crooks at a rally in Butler, Pennsylvania, on Saturday.
Trump, 78, told the convention at Milwaukee's Fiserv Forum KISS Melania is seen at last STUNT Hulk on Thursday night he found it "painful" to recall the shooting. He said he heard a "loud whizzing sound and felt something hit me really, really hard in my right ear".
Describing it as a "heinous attack", he added: "I said to myself, 'Wow, what was that? It can only be a bullet'.
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