Narendra Modi hailed the "special relationship" between the UK and India as he received a rock star reception from tens of thousands of supporters at Wembley stadium.
The Indian prime minister addressed up to 60,000 people gathered for a huge rally at the home of English football during his three-day visit to Britain.
The event came after Mr Modi had lunch with the Queen at Buckingham Palace and attended further meetings with business leaders as part of a trade drive.
It was also announced that the Duke of Duchess of Cambridge will go on a tour of India next spring.
Prime Minister David Cameron joined Mr Modi on stage at the Wembley extravaganza, which included performances from Indian and British performers and a fireworks display.
Mr Cameron was met by warm applause as he addressed the crowd and described the rally as a "truly historic moment".
He said: "It is the most spectacular celebration of British-Indian relations this country has ever seen.
"Prime minister Modi, you can see what I see every day - British Indians putting the great in to Great Britain.
"It won't be long before there's a British Indian prime minister in Downing Street.
"Team India, Team UK - together we are a winning combination."
Mr Modi received a standing ovation as he was introduced and declared "good evening Wembley!"
He said: "This is a historic day. Two great nations, two vibrant democracies - we are celebrating this very special relationship in this very special venue.
"It's been 12 years since I had been here. In that time a lot of water has gone down the Thames.
"As I stand here my countrymen have handed me a new responsibility. In order to fulfil this new responsibility I'm investing all my efforts.
"I would like to assure you that the dreams you have dreamt - and the dreams every Indian has dreamt - India is capable of fulfilling these dreams.
"There is no reason for India to remain a poor country."
Supporters waved Indian flags and chanted "Modi" throughout the speech.
Manoj Ladwa, a founding member of the Europe India Forum, which organised the event, said demand for tickets meant they could have filled another Wembley Stadium.
He said: "We started off looking at other venues that were 10,000, 15,000, but we realised the immense demand and the popularity of prime minister Modi.
"The only stadium that could accommodate prime minister Modi at this particular time is Wembley Stadium. We've got 60,000 people but we had at least 100,000 more people wanting to register."
Mr Ladwa said Mr Modi had a "vision for India" which had resulted in his huge popularity.
He said: "They see in prime minister Modi, especially after his tremendous election result last year, a man that is filled with hope and aspiration and somebody who is decisive.
"In a country that has suffered a lot because of corruption and misadministration, Modi is regarded as someone who is a clean politician and is somebody who delivers."
Mr Modi's visit to Britain has seen the unveiling of £9 billion of commercial deals between the two countries.
But he has faced protests over his record as chief minister of Gujarat - including over riots in 2002 when more than a thousand Muslims were said to have died.