U.S. television networks, making the projections, said Clinton was the victor in the state of Vermont.
The early victories for both in all three states were long predicted but not especially significant in a national race where opinion polls show Clinton has an edge. Polls also closed in the battleground states of Virginia and Georgia although there were no immediate results.
Voting was due to end in the vital battleground states of North Carolina and Ohio in 30 minutes.
Clinton led Trump, 44 percent to 39 percent, in the last Reuters/Ipsos national tracking poll before Election Day. A Reuters/Ipsos States of the Nation poll gave her a 90 percent chance of defeating Trump and becoming the first woman elected U.S. president.
In a campaign that focused more on the character of the candidates than on policy, Clinton, 69, a former U.S. secretary of state, and Trump, 70, a New York businessman, accused each other of being fundamentally unfit to lead the country.
Trump again raised the possibility on Tuesday of not accepting the election's outcome, saying he had seen reports of voting irregularities. He gave few details and Reuters could not immediately verify the existence of such problems.
Financial markets, betting exchanges and online trading platforms largely predicted a Clinton win, although Trump's team said he could pull off a surprise victory like the June "Brexit" vote to pull Britain out of the European Union.
Voters appeared to be worried about the country's direction and were seeking a "strong leader who can take the country back from the rich and powerful," according to an early reading from the Reuters/Ipsos national Election Day poll.
The poll of more than 10,000 people who voted in the election showed a majority worried about their ability to get ahead in life, with little confidence in political parties or trust in the media.
Some 15 percent of Americans who cast a ballot on Tuesday said it was their first time voting in a presidential election, up from 9 percent in 2012, according to the Reuters/Ipsos Election Day poll. The poll showed 13 percent of voters waited until the final week to make up their minds.
Also at stake was control of Congress, with Republicans defending a slight four-seat majority in the 100-member Senate. The House of Representatives, where all 435 seats were up for grabs, was expected to remain in Republican hands.
The Dow Jones Industrial Average index ended up 0.4 percent as investors bet on a win for Clinton, seen by Wall Street as more likely to ensure financial and political stability. Mexico's peso hit a two-month high on Tuesday on the expectation of a loss for Trump, who has vowed to rip up a trade deal with Mexico.
(Additional reporting by Emily Stephenson and Amanda Becker traveling with the candidates, Letitia Stein in St. Petersburg, Florida, Luciana Lopez in Miami, Doina Chiacu, Andy Sullivan and Susan Heavey in Washington, Colleen Jenkins in Winston-Salem and Kim Palmer in Ohio; Writing by Alistair Bell and John Whitesides; Editing by Howard Goller and Frances Kerry)
