Gukesh surpassed a record held by Russia's Garry Kasparov, who won the title at age 22, after clinching a dramatic endgame in Singapore to be crowned champion.
He also became the second Indian after five-time world chess champion Viswanathan Anand to hold the title.
Indian Prime Minister Narendra Modi led the tributes to what he described as a "historic and exemplary" achievement.
"Congratulations to Gukesh D on his remarkable accomplishment. This is the result of his unparalleled talent, hard work and unwavering determination," Modi wrote on social media platform X.
"His triumph has not only etched his name in the annals of chess history but has also inspired millions of young minds to dream big and pursue excellence. My best wishes for his future endeavours."
Anand, who played a mentor's role in Gukesh's remarkable journey, said the teenager had excelled.
"Congratulations! It's a proud moment for chess, a proud moment for India... and for me, a very personal moment of pride," Anand said on X.
The usually shy and reserved Gukesh burst into tears after nearly three weeks and 14 games of intense battle against the 32-year-old Ding.
Gukesh won the final game, which appeared to be heading towards a draw that would have necessitated further tiebreak matches, after pouncing on a blunder by Ding.
Indian sport shooter and Olympic gold medallist Abhinav Bindra said the teenager has "inspired a generation".
"Your brilliance, determination, and grace under pressure have made the entire nation proud," said Bindra.
"You've not just won a title but inspired a generation to dream big. Wishing you even greater success ahead!"
Born to a doctor father and microbiologist mother in the south Indian city of Chennai, Gukesh became India's youngest grandmaster aged 12 years, seven months and 17 days, and among the youngest in the history of the game.
He reached the world championship by becoming the youngest-ever winner of the prestigious Candidates Tournament in April.
