The British Prime Minister also said that a special tricolour flypast by the Red Arrows Royal Air Force (RAF) Aerobatic Team will take place in honour of his Indian counterpart.
"This is a special week for Britain and for India because of the extraordinary visit of Prime Minister Modi. I think it's going to be spectacular. We are going to see for the first time ever the Red Arrows fly with colours of the Indian flag coming out.
"What I hope we can achieve this week as we have this great visit is not to rest on the laurels of the past and the ties of history, language and culture, important as they are.
"Not simply to celebrate the immense economic ties, with India a top investor into Britain and Britain a top investor into India...But actually building a thoroughly modern partnership between our two great countries," he said.
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"But what I think is important is the future that we can have together. The future of the world's oldest democracy and the world's largest democracy," he added.
Cameron highlighted a stop at the Gandhi statue in Parliament Square among the many "important visits and many important discussions" to take place over the course of the three-day visit by Modi starting on Thursday.
"I don't know what magic that is as I struggle to fill Wembley town hall," he joked.
Stressing on the importance of India and the UK working together, he said: "We both face so many of the same challenges, whether it is fighting terrorism and Islamist extremism, which has done so much damage to India and to Britain.
"We must stand and have that fight together, whether it is fighting climate change, entrenched poverty, or finding jobs and livelihoods for our young people and growth in our cities. These are challenges that Britain and India can face together in a thoroughly modern partnership.