The service aimed at regular visitors, business travellers or skilled workers, but not students, will allow applicants at centres in Mumbai and Delhi to get hold of a six-month, multiple entry visa in just one day.
David Cameron unveiled the policy during the mission, and also took time out yesterday to play cricket on Mumbai's famous Oval Maidan.
The UK Government has faced criticism for deterring talented individuals and firms from coming to the UK as it tries to reduce net migration.
Student visa applicants from high-risk countries outside the EU will be interviewed to crackdown on bogus students, while a new test has been introduced to tackle foreign nationals attempting to enter the UK with fake firms.
However, Immigration Minister Mark Harper said: "We are committed to making the UK an attractive place to visit and a destination for the brightest and best to work and do business."
The Government said the new "super-priority" service, which will launch in March, was developed after discussions with prominent Indian businesses.
India remains Britain's biggest visa operation in the world, processing around 400,000 applications each year, with the vast majority approved and processed within 15 working days.
Last month, The Herald revealed how the Coalition's crackdown on student visas to stop people entering the UK illegally had resulted in a slump of 25% in undergraduates from Pakistan and India coming to Scottish universities.
Last night, Pete Wishart for the SNP accused Mr Cameron of "blatant hypocrisy" for welcoming Indian students to the UK while the Coalition's new immigration policy had caused a sharp decline in numbers.
He said: "International students were already going to tremendous lengths to comply with the UK Border Agency's immigration rules.
"The termination of the UKBA post-study work route – which was part of the visa package and enabled international students to help pay off their fees – has left Scotland unable to compete with many of our competitor nations who still offer the feature."
Heading the largest ever UK trade mission to India, comprising of more than 100 business leaders, the Prime Minister urged India to open up its markets in areas like insurance and banking to British companies.
He said Britain was incredibly welcoming to inward investment by Indian firms in historic names like Jaguar and Tetley Tea and was making it easier for Indian business people and students to come to the UK.
However, Mr Cameron stressed the process must "go both ways" and called on Delhi to sweep away barriers to trade which he said were antiquated.
He is being accompanied on his three-day trip by representatives from companies such as BAE Systems, Diageo, which owns the Johnnie Walker whisky label, architectural firm John McAslan, which has a base in Edinburgh, and Rolls-Royce.
He told his audience in Mumbai that he wants Britain's partnership with India to be "a really special relationship".
He said: "Britain wants to be your partner of choice. There are huge ties of history and language and culture and business but we have only just started on the sort of partnership we could build.
l Mr Cameron has admitted there are not enough women in Cabinet, saying he needed to do more to address the gender imbalance in Britain. He said: "My wife likes to say that if you don't have women in the top places, you are not just missing out on 50% of the talent, you are missing out on a lot more than 50% – and I think she probably has a point."