The result also means that Button's Brawn GP team have claimed the constructors' title.
Brawn GP also lead the constructors' championships as the traditional teams -- Ferrari and McLaren -- continue to struggle.
Brawn GP were created in the wake of Honda's withdrawal from Formula 1.
Brawn GP chief Ross Brawn had mounted a robust defense of his position.
The Formula 1 Teams Association (Fota) represents eight out of the 10 teams, including Ferrari, McLaren and championship leaders Brawn GP.
Branson has decided Virgin will get more value out of backing an underdog after sponsoring Brawn GP in their championship-winning debut season.
Button left Brawn GP after wrapping up his first title and how he shapes up against the precocious Hamilton will be monitored closely.
Branson was track-side as Brawn GP rounded off a sensational weekend with the top two podium spots following a frantic race in Melbourne.
Button led a Brawn GP one-two, with teammate Rubens Barrichello finishing second after starting third on the grid and running strongly at the start.
Independent F1 teams such as Brawn GP have supported the measures, with current championship leader Jenson Button telling BBC Sport he backed Mosley's budget cap.
Mosley upped the ante when he began legal proceedings against Ferrari, McLaren, Renault, BMW Sauber, Toyota, Brawn GP, Red Bull Racing and Toro Rosso on Friday.
The British team lodged a protest against the diffuser design used by Toyota, Williams and Brawn GP yet do not want to risk falling behind rivals.
The 40-year-old last raced in Formula 1 in 2006, but he has been strongly linked with a return to the sport with the renamed Brawn GP team.
BBC: Mercedes boss hints at F1 return for Michael Schumacher
And he admitted even he could barely believe his luck in Brawn GP grabbing a one-two barely 24 hours after he agreed to sponsor the former Honda team.
Seven members of the Formula One Teams Association, McLaren, Renault, Toyota, BMW Sauber, Brawn GP, Red Bull Racing and Toro Rosso gave Schumacher and Ferrari the green light.
He sits ninth in the 2009 drivers' championship, 42 points behind Brawn GP's English driver Jenson Button, while McLaren trail table-toppers Brawn by 73 points in the constructors' championship.
Massa has fully recovered from the injury, which happened after a spring that had become detached from Rubens Barrichello's Brawn GP car hit him just above his left eye.
Brawn GP's drivers Jenson Button and Rubens Barrichello occupy the first two places in the world championship heading into the Monaco GP with Button winning four of the five rounds.
Last season, Button and the Brawn GP team, helped by their revolutionary rear diffuser, won six of the first seven races, but experts are predicting a much closer tussle this year.
The Brawn GP team was rescued from the brink of bankruptcy by Brawn and Nick Fry after Honda withdrew from Formula One at the end of 2008 due to the economic downturn.
Furthermore, writs that had been threatened against Ferrari and the other teams in Fota - McLaren, BMW Sauber, Renault, Toyota, Red Bull Racing, Toro Rosso and Brawn GP - are likely to be shelved.
The result was a remarkable one for Brawn GP, who become the first debut team to finish one-two since 1954, when Juan Manuel Fangio led home Karl Kling for Mercedes in the French Grand Prix.
Button's Brawn GP team-mate Rubens Barrichello finished behind the dominant Red Bulls in third place, to close to within 23 points of Button in the world drivers' standings, with Vettel breathing down the Brazilian's neck.
Brawn GP drivers Jenson Button and Rubens Barrichello secured a one-two at the season-opener in Melbourne barely 24 hours after Branson confirmed a "substantial sponsorship" deal for the former Honda team, owned by Ross Brawn.
Red Bull looked set to begin the season in spectacular style at the Australian Grand Prix on Sunday with Sebastian Vettel tracking eventual winner, Brawn GP's Jenson Button, for the vast majority of the race.
If the top of the order was a surprise, so was the bottom five as Rubens Barrichello was 16th for Brawn GP, followed by Nico Rosberg in his Williams and Sebastian Vettel for Red Bull.
But that was no surprise as the 20 drivers grew accustomed to the track, culminating in the Finn ending up quicker than his McLaren team-mate by just 0.197 seconds, with Brawn GP's Button 0.234 seconds down on Kovalainen.
Alonso's quickest lap lifted him clear of second-placed Sebastien Buemi of Toro Rosso with local hero Rubens Barrichello of Brawn GP third -- as he aims for the victory that will keep his slim world title hopes alive.
Team principal Ross Brawn led a rescue package to buy out the team and continue work on Honda's 2009 car design -- the car would help Button win the world drivers' title and the constructors' championship for Brawn GP that season.
Formula 1's governing body and Fota have become embroiled in an increasingly bitter feud over Mosley's presidency and his plans for the 2010 season, which include budgetary and technical changes that have been met with opposition by Ferrari, Brawn GP, McLaren, Red Bull, BMW Sauber, Toyota, Renault and Toro Rosso.
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