He is also due to meet the Queen, visit a statue of Mahatma Ghandi and address crowds at Wembley Stadium.
Mr Cameron said the visit marked "a historic opportunity" for Britain and India to help each other prosper.
"It`s an opportunity for two countries, tied by history, people and values, to work together to overcome the biggest challenges of our age," Mr Cameron said.
"Prime Minister Modi and I intend to grab that opportunity with both hands."
Mr Modi, who will meet the Queen during his time in the UK, said the aim of the visit was to strengthen "co-operation with a traditional friend".
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