The win pushes the New York businessman closer to the Republican nomination for president, with 1,041 delegates.
A candidate must reach 1,237 delegates to become the party's nominee in November's general election.
His closest rival Mr Cruz earlier called him a "pathological liar" as the verbal blows reached a new intensity.
The Democratic race is still too close to call, with front-runner Hillary Clinton narrowly trailing Vermont Senator Bernie Sanders.
Indiana results as they come in
Mr Cruz and the third Republican in the race, John Kasich, had been hoping that Mr Trump, a New York businessman with no experience of elected office, would fall short.
That would have given them a chance to win at a contested convention in July, in which party delegates - officials and activists - vote for the nominee.
But Mr Trump only needs to win 43% of the remaining delegates to prevent that happening and win the nomination outright.
Turn out the lights, the party's over. Ted Cruz and the #NeverTrump movement threw everything they had at Donald Trump in Indiana, and it wasn't enough. It wasn't even close to enough.
They outspent him by more than a million dollars. Mr Cruz practically took up residence in the state for the past two weeks. He named Carly Fiorina as his running mate. Nothing worked.
If there was a defining moment of the Indiana campaign, it was Mr Cruz's fruitless attempt to reason with a group of pro-Trump supporters on Sunday. Every argument he advanced was rebuffed. Every bit of evidence of Trump malfeasance was denied. Mr Cruz was shouting in the wind.
In the coming days there will be a great reckoning, as the party comes to terms with the prospect of Mr Trump as their standard bearer in the autumn. Some will make peace. Some will despair. Others will say "I'm with her" and reluctantly move to Hillary Clinton's side.
It will be an unprecedented spectacle in modern US political history.
Mr Cruz had been pinning all his hopes on winning in Indiana, a state friendly to his social conservatism, and halting the momentum of Mr Trump.
The Texas senator and Mr Kasich even struck a deal that involved the Ohio Governor giving Mr Cruz a clear path in Indiana, in return for getting a clear path himself in later state contests.
Donald Trump is on course to win Indiana’s Republican presidential primary, dealing a huge blow to Ted Cruz's hopes.