Mr Trump, unpopular with many in his own party, now has a clear path to the 1,237 delegates needed to claim his party’s crown.
That would mark a stunning victory for a businessman few took seriously when he launched his campaign last year.
Bernie Sanders has defeated Hillary Clinton in Indiana’s Democratic race.
He trails Mrs Clinton in the all-important delegate count but after this victory he said the contest was still alive.
“Clinton campaign thinks this campaign is over. They’re wrong,” he said.
Mr Cruz’s advisers had targeted Indiana as the Texas senator’s best hope of halting Mr Trump’s march to the nomination.
“We gave it everything we’ve got, but the voters chose another path,” he told supporters in Indiana.
His departure means Mr Trump is now the presumptive Republican nominee, with plenty of state contests this month and next to reach the 1,237 delegates required to win.
The New York businessman is the first nominee since Dwight Eisenhower in 1952 to lack any previous experience of elected office.
Ohio Governor John Kasich has vowed to remain in the Republican race, but trails far behind Mr Trump in terms of delegates.
“It is a beautiful thing to watch, and a beautiful thing to behold,” Trump said during a victory speech. “We are going to make America great again.”
He praised Mr Cruz as a “tough, smart competitor”, which marked a sharp reversal in tone after a day when the two men slung mud at each other from close quarters.
The verbal attacks reached a new level of intensity when Mr Cruz attacked the billionaire businessman as a “pathological liar” and “serial philanderer”.
That was provoked by a bizarre claim from Mr Trump that Mr Cruz’s father was linked to one of the most traumatic episodes in US history, the assassination of President John F Kennedy.
It is now increasingly likely that Mr Trump will face Mrs Clinton in the autumn in the battle to succeed President Barack Obama, who will be leaving the White House after two terms.
But Republicans have expressed reservations about Mr Trump’s outspoken remarks, which have offended women and Hispanics.
There are also concerns about some of his policies on immigration and national security, like building a wall on the southern US border paid for by Mexico, a ban on Muslims coming to the US and the killing of the families of terrorists.