India won the three-match series 1-0 after the final Test ended in a draw at the Oval on Monday. The tourists had won the second Test at Trent Bridge after being saved by rain in the drawn first Test at Lord's.
It was only the third series win by India in England following the 1-0 win by Ajit Wadekar's team in 1971 and the 2-0 victory by Kapil Dev's men in 1986.
Indian cricket board chief Sharad Pawar hailed the win and announced a bonus of 10 million rupees (250,000 dollars) for the 16 players, interim manager Chandu Borde and assistant coaches Robin Singh and Venkatesh Prasad.
"I would like to congratulate the Indian contingent for their excellent teamwork and performance against England in the Test series," Pawar said in a cricket board statement.
"I am sure every Indian will feel proud of our players, who have won a series in England after a gap of 21 years. I am sure a similar performance will be shown in the one-day series."
The seven-match one-day series starts at the Rose Bowl on August 21.
The series success was marred by widespread criticism of Dravid's decision not to enforce the follow-on on the fourth day despite being 319 runs ahead, allowing England an escape route from defeat.
England, set an improbable victory target of 500, batted out the last 110 overs to make 369-6 in their second innings and force a draw, but still lost their first Test series at home since 2001.
Dravid defended his decision, saying he did not want to tire out his three-man seam attack of Zaheer Khan, Rudra Pratap Singh and Shanthakumaran Sreesanth, and lone spinner Anil Kumble.
"As a captain I get a pulse for what's happening," the Indian captain said. "I have to back my judgment -- that is what I earn my corn for."
The Indians, who suffered the humiliation of being knocked out in the first round of the World Cup in March, have now won their fourth consecutive Test or one-day series.
Dravid's men defeated World Cup nemesis Bangladesh 1-0 in the Tests and 2-0 in the one-dayers in May before winning a one-day series 2-1 against South Africa in Ireland the following month.