An international tribunal reprimanded Mercedes and Pirelli for breaking the rules on testing and ordered the British-based team to miss a three-day young driver test scheduled for Silverstone in July.
The verdict, announced by the governing International Automobile Federation (FIA) in a statement after a seven-hour hearing in Paris on Thursday, was accepted with relief by the team led by Formula One veteran Ross Brawn.
"Mercedes accepts the proportionate penalties of a reprimand and suspension from the forthcoming young driver test," they said in a statement, adding that they would not appeal.
"We now wish to bring this matter to a close and focus on the forthcoming British and German Grands Prix, both of which are important home races for the team."
The tribunal had the power to impose a heavy fine, dock points or even ban Mercedes from the world championship - although that was never a likely option for one of the sport's major players who are currently third overall.
Champions Red Bull, who had protested to the FIA at last month's Monaco Grand Prix when they found out Mercedes had used their current car and drivers in the test, had indicated they wanted to see a tough response.
"Usually if you commit a sporting offence there's a sporting penalty that goes with it," team principal Christian Horner said after the hearing.
The tribunal ruled in its detailed written verdict that Mercedes had not intended to obtain any unfair sporting advantage by taking part in a tyre test at Barcelona's Circuit de Catalunya after the Spanish Grand Prix.
Teams are banned from track testing during the season but Pirelli, who are the sole tyre suppliers and not competitors, are allowed to do so with a representative car.
Both Mercedes and Pirelli had said the test was private, not secret, and denied accusations the team had gained an unfair advantage from it.
"Neither Pirelli nor Mercedes acted in bad faith at any material time," the tribunal said, declaring that both parties had disclosed to the FIA 'at least the essence' of what they intended to do and had sought permission.
"Mercedes had no reason to believe that approval had not been given," it said, finding that FIA technical head Charlie Whiting had also acted in good faith after taking advice from the FIA's own legal department following separate conversations with Brawn and Mercedes sporting manager Ron Meadows.
Mercedes were found to have acted in breach of the rules, with the tribunal saying they did gain some material advantage as a result of their test with both 2008 champion Hamilton and subsequent Monaco winner Rosberg on track.
Mercedes, Pirelli and the FIA were ordered to pay a third each of the costs of the investigation and procedure with the FIA paying all their own legal costs.
"We are satisfied with the outcome because it shows the court recognised Pirelli has always acted in good faith," said a Pirelli F1 spokeswoman.
Being barred from the young driver test was suggested by the team themselves on Thursday as a possible means of redress if the tribunal felt a sanction needed to be imposed.
While it will mean losing out on three useful days of track testing, it will fall hardest on British reserve driver Sam Bird who would otherwise have expected some rare time in the car.
The FIA hoped lessons would be learnt from a case that was the first to be sent to the tribunal, set up in 2010 to deal with issues that race stewards were unable to rule on.
"To this end, the FIA will make sure, in association with all F1 teams, that its control of the testings is strengthened," it added. Mercedes said they looked forward to working with the FIA and rival teams "to establish a more rigorous procedure".
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