
India lost two of their first three games in the series, including one against Sri Lanka, who lost last April's World Cup final to Australia.
But the team battled back to pip Sri Lanka for a place in the best-of-three finals series, going on to beat Australia 2-0.
India last won an important limited overs series in Australia 23 years ago.
Triumph Against All Oz, headlined the Hindustan Times newspaper on Monday.
"The Men in Blue overcame insult and injury, hostility on and off the field from players, spectators and media, on the world's toughest tour against the world's best side," the paper said.
"Australian captain Ricky Ponting admitted India outplayed them in the one-day finals. A more graceful captain would also have admitted that India had out-behaved Australia all summer."
Controversy
A race row and umpiring controversy had earlier threatened to disrupt the cricket tour.
The controversial Sydney Test was blighted by contentious catches, a series of poor umpiring decisions and over-zealous appealing.
Hours after it finished, Indian spinner Harbhajan Singh was banned for three matches for an alleged racist remark against Andrew Symonds
Singh had denied the charge and the Indians threatened to abandon the tour.
The charge of racially abusing Symonds was later downgraded to abusive language by the International Cricket Council (ICC).
The ICC also accepted India's demand that West Indian umpire Steve Bucknor be removed for the rest of the series after the umpiring fiasco in Sydney.
We Are The Champs, headlined The Times Of India.
"MS Dhoni (India captain) and his men have probably accomplished even more. They may have signalled an impending change in the world cricketing order, while wrecking the aura of Australian invincibility," the paper said.
"India has long had the financial clout. But now, with cricketing muscle lending that support, the power equations in the game seem to be shifting."
They bury the biggest ghost, headlined The Indian Express.
"For Indian cricket this is a red letter day. This young side has done what no other Indian team has done before - a series victory against Australia."
Cricket website Cricinfo said: "India irritate Australia's senior men in a way no other team can manage and the uneasy relationship adds to the home side's confusion."
Indian PM Manmohan Singh complimented the team on its victory.
"It is a fabulous victory. This is victory based on teamwork and strong determination," he said.
The Indian cricket board has announced cash awards to the members of the winning team.
Source: BBC (South Asia Edition)