In a speech to Parliament, he said the two countries needed to create "one of the leading global partnerships".
Mr Modi and David Cameron are due to sign deals between Indian and UK firms worth more than £9bn.
The leaders said they would collaborate on issues including finance, defence, nuclear power and climate change.
Mr Modi, whose three-day visit is the first by an Indian prime minister in a decade, said India's relationship with the UK was of "immense importance".
He also said that India viewed the UK as its "entry point to the EU".
Mr Modi is known as a brilliant public speaker and is very popular among Indian communities abroad - 60,000 people are expected to fill Wembley Stadium to hear him speak