The International Automobile Federation (FIA) had been investigating after Mercedes and Red Bull raised concerns about what Ferrari were doing.
FIA race director Charlie Whiting told a small group of British reporters and Reuters on Saturday that Ferrari's system was more complicated than that used by rivals but he now accepted everything was above board.
"We had some concerns in Baku (at the Azerbaijan Grand Prix in April) that were difficult to explain and we worked through it with them," said Whiting at the Monaco Grand Prix in a meeting also attended by FIA president Jean Todt.
"(The rulebook) says that it is the duty of the competitor to satisfy the FIA that their car complies at all times and they were having difficulty satisfying us," he added.
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"Here, we are now satisfied."
Whiting noted that a senior Ferrari engine designer had moved to Mercedes this season and said former Ferrari technical head James Allison, now in a similar role at Mercedes, had raised concerns.
"The matter was exacerbated by unsubstantiated speculation that went through the paddock like wildfire," added Whiting.
He said any information that might have travelled from Ferrari to Mercedes was likely to have been outdated.
Paddock gossip has suggested Ferrari, the sport's most successful and oldest team, were somehow circumventing the regulations.
Ferrari had refused to comment on media speculation.
The controversy burst out into the open on Thursday, however, when the official Formula One website reported that the FIA had asked Ferrari to "run an extra piece of hardware" so they could monitor the system.
The website suggested rivals had expressed concerns Ferrari might be boosting energy flow beyond the permitted limit.
Whiting said the FIA had seen initially "some things in the data we could not quite explain... we went through it with Ferrari and they gave explanations which were not particularly convincing.
"We wanted to really get to the bottom of it and in Spain (two weekends ago), they took some measures to make sure we understood it more and that we were seeing things that we were happy with."
He said former Renault engine expert Cedrik Staudohar, now working for the FIA, had played an important role in the technical probe.
Todt, a former Ferrari boss, said he had first heard about the problem after the race in Baku and that any rivals with concerns should have aired them openly.
"If a team has some doubts, they could have made a protest," he said. "It would be much more healthy rather than to manipulate the press to address the problem."
(Editing by Clare Fallon)
