Clinton, however, suffered an upset defeat at the hands of Bernie Sanders in Indiana but the outcome was unlikely to slow the 68-year-old former secretary of state's march to the Democratic nomination.
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"I am honoured to be the presumptive nominee for the Republican Party. It is time to unite our party and defeat Hillary Clinton," Trump said in a message to his supporters after winning the Indiana primary.
Cruz, who has engaged in a bitter and nasty war of words with Trump, announced his decision to drop out of the race even when the counting of votes was still on.
69-year-old Trump, who now needs less than 200 delegates to reach the magical figure of 1,237 delegates to become the Republican presidential nominee still faces opposition from Ohio Governor John Kasich, who has less than 200 delegates.
Kasich has made it clear that he is not dropping out of the race.
After Trump's win, the Republican National Committee (RNC) chairman Reince Priebus said that Trump would be the presumptive nominee.
"We are going to make America great again," a confident Trump told supporters at his campaign headquarters in New York as he announced to take on Clinton.
"We are going after Hillary Clinton. She will not be a great president. She will not be a good president. She would be a poor president. She does not understand trade," Trump said, giving a brief glimpse of his campaign against the Democratic presidential nominee.
Talking about Cruz, Trump described him as a tough competitor and appreciated his decision to withdraw from the race.
"I want to congratulate Ted Cruz. He is a tough smart competitor," he said of the Texas Senator with whom he had a bitter exchange of words hours before the result of the Indiana primary.
"Ted Cruz is one hell of a competitor. He is an amazing guy. He has got an amazing future. He is one tough competitor," Trump said.
In his speech that lasted for a little less than 20 minutes, Trump talked about uniting the party and focusing on trade and economic issues.
"We are going to bring back our jobs," Trump said as he warned the US companies with "consequences" if they moved out of the country.
Trump, a New York-based real estate mogul who made money from constructing buildings and a popular reality television star, joined politics about 10 months ago with political pundits giving him not much of a chance to make it this far.
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