Rahul Dravid's side wrapped up the tense fourth and final Test in Jamaica by 49 runs on Sunday after largely dominating the struggling Caribbean side in the series.
It was India's first major Test series victory outside the south Asian region since Kapil Dev skippered the team to a 2-0 triumph in England in 1986.
The series win was also the first in the Caribbean for 35 years.
Kapil led the praise on Monday, after millions of Indian fans sat up to watch the game on television until the early hours.
"Winning is beautiful," he told Reuters. "The boys have finally tasted the feeling of winning abroad. I am very happy."
Despite their formidable home record, India has been criticised for a modest overseas record with a 4-1 upset in the preceding one-day series piling more pressure on the tourists.
Since 1986, India's only Test series success outside the sub-continent was last year's 2-0 sweep against lowly Zimbabwe, with other best efforts being draws in England in 2002 and in Australia the following year.
DRAVID HAILED
Former Test captain Ajit Wadekar lavished praise on Dravid, who prospered with the bat on an unpredictable Sabina Park pitch and also marshalled a raw pace attack throughout the series.
His invaluable knocks of 81 and 68 earned him the man-of-the-match accolade. He was also named the player of the series after aggregating 496 runs at an average of 82.66.
"It was the captain who led from the front," said Wadekar, who led the team on their previous series victory in the Caribbean in 1971.
"It was his efforts, he shouldered the responsibility and pushed the boys," Wadekar added.
Leg-spinner Anil Kumble grabbed six for 78 to spin India to victory, sharing 14 wickets with off-spinner Harbhajan Singh.
India had won just three Tests out of 41 in West Indies and none in Jamaica, where they lost six of the previous nine games.
Wadekar put the victory in perspective against a West Indies side who have struggled in the last few years and barely staved off defeat in the first two of the three drawn Tests.
"Looking at the opposition we should have won one or two more Tests," he said. "We looked like a team in this Test and played as a unit."
India were without the injured Sachin Tendulkar and both Dravid and coach Greg Chappell came under pressure after failing to win until the very end.
Kapil was among the former players who criticised the exclusion of young all-rounder Irfan Pathan, who played only one Test after struggling in the one-dayers, and Harbhajan, who came in for the final two Tests.
"Realisation seemed to have dawned that Harbhajan and Anil (Kumble) should be played in tandem," Wadekar said.
