The 35-year-old Dravid became only the sixth player to reach the landmark while scoring 111 for his 25th century on day four of the first Test against South Africa.
Dravid also became only the third player to achieve the landmark in both Tests and one-dayers, joining compatriot Sachin Tendulkar and West Indies batsman Brian Lara.
“It is a proud moment,” he told reporters. “For me, growing up, I dreamt of playing for India. When I look back I probably exceeded my expectations with what I have done over the last 10 to 12 years.
“I can look back and reflect that I maximised my potential over these years,” he said. “To do it in Chennai with my family and friends watching was great.”
Dravid said he remembered as a boy when Sunil Gavaskar (10,122 in 125 Tests) became the first to reach the mark, with a late cut against Pakistan in the Ahmedabad Test in 1987.
“I never had an ambition to do it because I never believed,” he said. “It is just a reflection of my longevity in the game.”
Lara, who retired after playing the 2007 World Cup in the West Indies, leads the 10,000-run Test club with 11,953 runs in 131 Tests. Tendulkar, who failed to score on Saturday, has made 11,782 runs in 147 Tests.
Former Australian captains Allan Border (11,174 in 156 Tests) and Steve Waugh (10,927 in 168 Tests) are the other two players to score 10,000 Test runs.
“For me to be in that company is surreal in some ways,” Dravid said. “I know Ricky Ponting and Jacques Kallis, the other two great batsmen of my generation, are also probably going to get there very soon.”
He was disappointed that opener Virender Sehwag could not break Lara's world record for the highest score (400 not out) after he was dismissed for an Indian-record 319 on Saturday.
“We knew if Viru batted for a couple of hours he would get close to it, if not pass it,” he said. “He has always batted positively that is why he has been able to score that way.”—Agencies