On his 35th birthday, Kohli made an undefeated 101 as India reached 326-5 in their World Cup group game with South Africa at the country's iconic Eden Gardens in Kolkata.
It had taken him 277 innings to score 49 hundreds at this level compared to the 438 required by Tendulkar.
"Every opportunity to play for India is a big one and to do this on my birthday in front of a huge crowd is the stuff of dreams. It is something you dream about as a child," said Kohli.
"I am just happy to help the team as much as possible."
In all Kohli now has 49 ODI centuries, 29 hundreds in Test matches and one ton in Twenty20 internationals.
He has accumulated more than 26,000 runs in all three formats.
"Well played Virat," wrote Tendulkar on X, formerly Twitter, who celebrated his 50th birthday in April.
"It took me 365 days to go from 49 to 50 earlier this year. I hope you go from 49 to 50 and break my record in the next few days. Congratulations!"
Former rival, Pakistan's Shahid Afridi also hailed Kohli.
"This is the best birthday gift from Virat Kohli to the fans of team India & entire cricket fraternity," wrote Afridi on X.
Former West Indies fast bowler Ian Bishop, now a respected TV commentator, wrote on social media: "Legacy cemented: Century No 49 on his 35th birthday for Virat Kohli to draw level with the great Sachin Tendulkar. Two greats of the game."
Suresh Raina, who once played alongside Kohli, described his compatriot as "so elegant".
"When I first met him, I remember every game he would say, 'I have to score a 100 today'. Well done Virat, so beautiful, so elegant, just looking like a wow!"
In a Star Sports broadcast on Sunday, former India all-rounder Irfan Pathan said in Hindi: "Kohli carried Sachin on his shoulders during the 2011 World Cup celebrations....."
"But now he stands shoulder to shoulder with the Master Blaster."
Former India opener Virender Sehwag told Kohli "to take a bow".
"What a day to equal the great man's record of most ODI 100s. His birthday at the historic Eden Gardens. Take a bow, Virat Kohli. Congratulations on a great one," wrote Sehwag.
Carlos Braithwaite, the West Indian star who famously clubbed four sixes in the final over to beat England in the 2016 Twenty20 World Cup final in India, said he hoped Kohli would hit a record 50th century -- at the appropriate time.
"You want Kohli to get the record in the semi-finals or final. It wouldn't be romantic to do it against the Netherlands," he said on the BBC.
However, the significance of the occasion appeared to have little effect on Sri Lanka's World Cup skipper Kusal Mendis.
Addressing a press conference in New Delhi ahead of his team's game against Bangladesh, Mendis was asked if would like to pass on his tribute to Kohli.
"Why I would congratulate him?" asked a bemused Mendis.