The New York billionaire won decisively in a state where Cruz, his nearest rival, had hoped to show he was still a factor in the race for the Republican nomination.
Republican National Committee Chairman Reince Priebus called Trump the party's presumptive nominee in a tweet and said, "We all need to unite and focus" on defeating Clinton.
As the vote returns flowed in, Cruz announced that he has ended his campaign at an event in Indianapolis, with his wife, Heidi, at his side. Cruz, 45, sounding beaten but defiant, said he no longer sees a viable path to the nomination.
"Together we left it all on the field in Indiana," said Cruz, a U.S. senator from Texas. "We gave it everything we got. But the voters chose another path, and so with a heavy heart, but with boundless optimism for the long-term future of our nation, we are suspending our campaign."
Trump was on track to take over 50 percent of the vote. Ohio Governor John Kasich was running a distant third.
On the Democratic side, Bernie Sanders was leading Hillary Clinton by a modest margin, but the race was still considered too close to call.
Cruz had been counting on a win in Tuesday's primary to slow the New York businessman's progress toward the nomination. But Trump rode momentum from wins in five Northeastern states a week ago to wrest Indiana from Cruz, whose brand of Christian conservatism had been expected to have wide appeal in the state.
David Yepsen, director of the Paul Simon Public Policy Institute at Southern Illinois University, said the Republican race is over.
"Cruz is certainly young enough to fight again another day. Kasich's a serious guy but if stays in this he could look silly," Yepsen said.
The loss for Cruz was a sour ending to a rough day in which he got entangled in a harsh back-and-forth with Trump.
It began when the billionaire repeated a claim published by tabloid newspaper the National Enquirer that linked Cruz's father, Cuban emigre Rafael Cruz, with President John F. Kennedy's assassin Lee Harvey Oswald.
Campaigning in Evansville, in the state's southwest corner, Cruz sounded deeply frustrated by the bombastic real estate mogul, who has ripped Cruz at every turn.
"The man cannot tell the truth but he combines it with being a narcissist," Cruz said, "a narcissist at a level I don't think this country has ever seen."
Cruz termed Trump a "serial philanderer" - likely as part of his strategy to try to win the support of evangelical voters. Trump, in response, said Cruz had become "more and more unhinged."
The only hope Kasich has for becoming the Republican nominee is to somehow deny Trump the 1,237 delegates he needs to win the nomination outright and force Republicans at their July convention in Cleveland to choose one of them.
Kasich vowed to stay in the race.
"Tonight’s results are not going to alter Gov. Kasich’s campaign plans," Kasich senior strategist John Weaver said in a campaign memo. "Our strategy has been and continues to be one that involves winning the nomination at an open convention."