India and the United States have built close political and security ties and Trump's two-day trip is a sign of their converging interests, officials say, including a way to counter China's rise as a superpower.
Prime Minister Narendra Modi was at the airport to greet Trump and his wife, Melania, as they stepped off Air Force One.
A road show is planned and a huge reception will be held in a 110,000-seat cricket stadium in the city which is the political home of Modi.
A huge crowd has filled the stadium, claimed to be the world's biggest cricket ground.
In the stadium, many people were wearing customised white hats saying "Namaste (Greetings) Trump", while workers handed out thousands of cardboard masks of the U.S. president.