At 24 years and 98 days, Vettel is the youngest double champion in history.
Among those to congratulate Hamilton was former McLaren team-mate and double world champion Fernando Alonso.
Training partner, Jon Drummond, has warned Greene's rivals not to underestimate the Olympic and double world champion.
And he conceded he could be suffering for his lack of experience, compared to the double world champion.
"Our efforts were helped by particularly favourable weather with sunshine and summery temperatures, " explained the double world champion.
CNN: Vettel off to a flier as Red Bull set the pace in Melbourne
Double Olympic champion Haile Gebrselassie failed to finish after suffering an asthma attack.
Double world champion Alonso won the race -- the first for Renault in two years -- despite starting from 15th on the grid.
Double world champion Fernando Alonso was fourth fastest, edged out by his Ferrari teammate Felipe Massa who went third fastest at the Sepang International Circuit.
The 1998 double Olympic champion was badly injured in August 2001 in a motorbike accident and did not resume competitive skiing again until January 2003.
Japan meanwhile were celebrating after landing their first Olympic swimming title for 12 years when double world champion Kosuke Kitajima won the men's 100m breaststroke.
Double world champion Alonso of Spain won the race -- the first for Renault in two years -- despite starting from 15th on the grid.
CNN: Ex-Renault chief Briatore wins appeal over lifetime F1 ban
Double Masters champion Jose Maria Olazabal has also comfirmed his entry.
Hamilton has become a hate figure for some Spaniards because of his rivalry with the country's double world champion Fernando Alonso when they were team-mates at McLaren.
Renault's Fernando Alonso chose the same tactic a lap later and it secured the double world champion the fourth place he had held for much of the race.
Tancock triumphed for England in the 100m backstroke , the previous race in a medal-packed Friday programme, and declared it "pretty cool" to be a double Commonwealth champion.
Double world champion Alonso looked set to top the times with an impressive lap set in the morning but the German beat him by 0.023 seconds later on.
Usain Bolt: The man whose name sounds preordained by the Gods, a real-life superman, the greatest sprint showman that ever lived, the world-record holder and the newly crowned double Olympic champion.
News of the bonding session came in a statement issued by McLaren on behalf of Hamilton to set the record straight over the British rookie's relationship with double world champion Alonso.
In double world champion Fernando Alonso's final appearance for Renault before he leaves for Ferrari, the Spaniard suffered the worst qualifying session of his underwhelming season to finish down in 16th.
Lotus have a rich history in F1, with a list of former drivers which includes British double world champion Jim Clark, Austrian 1970 title winner Jochen Rindt and legendary Brazilian racer Ayrton Senna.
It comes after a run of terrible luck for the double world champion at the last two races, when Ferrari have not been able to deliver on a major improvement in performance from their car.
Teammate Lewis Hamilton looked in good shape on Saturday, getting around the track in 1 minute 20.558 seconds, while double world champion Fernando Alonso set a fastest time of 1 minute 20.494 seconds in his Ferrari.
With the combined efforts of Webber and double world champion Sebastian Vettel, Red Bull currently hold an imperious lead at the top of the constructors' championship, 64 points ahead of Ferrari, who have failed to finish top since 2008.
France 0, Spain 1: For the first time in years, there was a hint of doubt about Spain this week, a sense that the most dominant side in the world, the double European champion and World Cup holder, was finally fallible.
For double world champion Alonso the close of 2007 marked the finale of a nightmarish year at McLaren where he and Hamilton traded barbed insults in the media before doing their best to pretend the other did not exist.
Rosberg, who has scored all of his team's 25.5 points so far this year, was a target of Mercedes-powered McLaren two years ago when they were looking for a replacement for double world champion Fernando Alonso but he was bound by his existing contract.
That honour fell to Ferrari president Luca di Montezemolo, whose chaotic announcement of a five-year sponsorship deal with Spanish bank Santander - which became a McLaren sponsor during Fernando Alonso's brief stint with the team - prompted speculation he would also confirm the double world champion's widely-anticipated move to Ferrari in 2010.
The Spanish double world champion, whose presence at the test drew a huge crowd and led to traffic jams on the way to the track, improved to a 1:20.966 on his next run and then 1:20.493 - just 0.1secs off the fastest time of the test so far, set by Schumacher on Friday.
BBC: Nick Heidfeld heads Fernando Alonso at his Renault test
Williams is a double Grand Slam champion, twice a Lions tourist and set to break Wales' cap record.
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