Polls in the eastern time zones of Indiana and Kentucky were the first to close, and a flood of vital battleground states such as Virginia, North Carolina and Ohio — where polls were due to close before 11:30am AEDT — will provide initial clues of the possible winner.
Mrs Clinton led Mr Trump, 44 per cent to 39 per cent, in the last Reuters/Ipsos national tracking poll before Election Day.
A Reuters/Ipsos States of the Nation poll gave her a 90 per cent chance of defeating Mr Trump and becoming the first woman elected US president.
A strong turnout of voters for Mrs Clinton could jeopardise Republican control of the US Senate, as voters choose 34 senators of the 100-member chamber.
Democrats needed a net gain of five seats to win control. All 435 seats in the House of Representatives was being contested.
The House is expected to remain in Republican hands.