He has won Florida, Ohio and North Carolina, while Democratic nominee Mrs Clinton took Virginia, ABC projects. Pennsylvania is too close to call.
The race is deadlocked in Michigan, which has not voted for a Republican White House candidate since 1988.
Markets lurched as Mrs Clinton's path to victory seemed less assured.
The US dollar and Mexican peso plummeted while the Dow futures dropped more than 650 points.
Mr Trump's Ohio win was a big boost to him, as no Republican has ever taken the White House without winning the Midwestern bellwether.