"The long march to liberty is now being matched by the rapid march towards prosperity," Brown said in his article, published in Asian Lite magazine.
Brown said modern Britain "simply wouldn't be the same without our strong bond with India and the enormous part played by the Indian community."
"The relationship of one of the world's oldest democracies with one of the largest owes its foundations to our proud historic ties.
"But it thrives now - as a partnership of equals - on our shared values and our faith in free institutions, free markets and free societies."
The British leader said his meetings with prominent Indian-origin people at a Diwali reception at 10 Downing Street in October "reminded me again of the deep respect and enduring friendship of our two nations."
"For many years now our public services, professions, businesses and cultural and creative industries have been enriched by the Indian community," he added.
"The Britain-India link is central to our shared prosperity and people of Indian origin here are part of the very fabric of modern British society."