Honda quit F1 in December, citing falling car sales and the global financial crisis.
They have bought the Brawn team that last year won the drivers' and constructors' championship in their debut season, after former owner Honda quit F1.
Honda's F1 team endured a deeply disappointing 2008 season on the track, earning just 14 points to leave them the lowest of the nine points-scoring teams.
The packages come after Japanese manufacturer Honda pulled out of F1.
Bridgestone becomes the latest Japanese corporation to quit high-end motorsport, with Honda's withdrawal from F1 at the end of last season setting the trend.
Japan's Sato, who has raced for Jordan, Honda and Super Aguri in F1, set the fastest times of the three at Spain's Circuit de Catalunya.
After the Honda motor company pulled out of F1 earlier this month, blaming the world economic crisis, the team are trying to find a buyer to continue in the sport.
The Brawn team raced as Honda last season but secured their survival only at the beginning of this month following Honda's decision to quit F1 because of the global financial crisis.
"We were just happy to get to Melbourne, there was nothing left in the cupboard - the car we had in Melbourne is the car we have now, " Brawn said, recalling the team's battle to survive in F1 following former owner Honda's decision to quit last December.
If no buyer is found, Honda's decision to quit will leave F1 with just 18 cars on the grid next season.
Honda's demise would also reduce the F1 grid to just 18 cars (nine teams) and would see them become the second team to fold this year following Super Aguri's closure early in the season.
F1 chief Bernie Ecclestone has now backed Honda to return to the front of the grid in partnership with McLaren, which lost former world champion Lewis Hamilton to Brawn's Mercedes team after last season and has struggled this year.
But with no money coming in, car sales down and an expensive new technologies coming for 2009, Honda felt they had no choice but to close their F1 operation.
The Brawn team was formed out of the ashes of the former Honda outfit after the Japanese car giant pulled out of F1 last December as a result of the global financial crisis.
Honda's case was slightly different to the rest of the F1 pack because they have run without sponsorship for the past two seasons.
The Virgin boss has hinted he could back an F1 team, but refused to confirm a direct link with Honda.
Klien, 27, has raced in F1 for both Jaguar and Red Bull and has been a test driver for Honda and BMW Sauber.
BMW, DaimlerChrysler, Renault, Honda and Toyota revealed their proposals for a Grand Prix World Championship (GPWC) at a meeting with nine F1 teams.
BBC: SPORT | Motorsport | Formula One | Rival series issues team pledge
The move brings a Japanese road-car manufacturer back into F1 for the first time since Toyota quit at the end of the 2009 season - which followed Honda's withdrawal a year earlier.
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