Tendulkar, who turns 39 next month, achieved the feat with a century in an Asia Cup match against Bangladesh at the Sher-e-Bangla stadium in Dhaka, ending a nervous wait of more than a year for millions of fans.
The Mumbai batsman, who has compiled more Test and one-day runs than anyone in history, reached the milestone with a single, marking the moment with a modest glance to the sky while pointing to the Indian flag on his helmet.
Tendulkar, already a legend of the modern era and one of the greats of all time, made 114 off 147 balls with 12 fours and a six, before he was caught behind off seamer Mashrafe Mortaza in the 47th over.
"It has not sunk in yet," he told the Neo Cricket channel, who are broadcasting the Asia Cup matches.
"I was not thinking about the milestone. The media started all this. In the restaurant, room service, everyone was talking about the 100th hundred," he added.
Tendulkar is the most capped player in the history of the game with 188 Test and 462 one-day appearances since making his debut against Pakistan in Karachi in November, 1989.
He has scored 49 one-day hundreds and 51 centuries in Test matches.
The father-of two, known variously as the "Little Master" or "Bombay Blaster", is worshipped as a demi-god in his cricket-crazy country and has barely put a foot wrong since he burst on the world stage in 1989, aged 16.
"I join the nation in congratulating Sachin Tendulkar on his making history -- a hundred centuries. He has made India proud," Indian Prime Minister Manmohan Singh said as the country celebrated.
He scored his 99th ton during a World Cup match against South Africa in Nagpur on March 12 last year, but failed to add to the tally on subsequent tours of England and Australia and a home series against the West Indies.
International Cricket Council chief executive Haroon Lorgat also lauded Tendulkar's achievement.
"On behalf of every cricket fan around the globe, I congratulate Sachin on becoming the first person to score 100 centuries for his country," Lorgat said in a statement.
"This is indeed a magnificent feat and not likely to be easily emulated. The number 100 is special for a batsman and to record 100 centuries for your country is a massive statement.
"He is a marvel to cricket lovers around the world and with an array of batting records, Sachin is a true role model who will undoubtedly hold a special place in cricket's history," Lorgat said.
Former Australian captain Ricky Ponting is the second batsman on the all-time list with 71 international centuries.