But the storm clouds have not all passed from this unlikely area of turbulence, with the Met Office acknowledging that the seven-month investigation into the allegations had uncovered management problems and that changes would have to be made.
Mr Giles launched the appeal earlier this month after the inquiry found him guilty of "serious misconduct". He told a two-hour hearing that the allegations against him, made principally by colleague Richard Edgar, were a "farrago of unrelated personal gripes" and did not amount to "serious misconduct".
The weatherman, who leads the BBC's team of 21 weather presenters and who received an OBE four years ago, had said that grumbles from performers with big egos had been exaggerated and blown out of all proportion.
He was telephoned with the result in Geneva yesterday as he attended the 50th-anniversary celebrations of the World Meteorological Organisation. Speaking through his union, the Institute of Professionals, Managers and Specialists, (IPMS) Mr Giles expressed his delight at the outcome.
"I have just spoken to Bill and he said he is very relieved at the decision and looking forward to going back to work on Monday. He says the sun is shining in Geneva," said union representative David Luxton.
Mr Edgar and fellow weatherman David Lee, who made a separate complaint, have been on sick leave since objecting to Mr Giles's management style in March. They claimed that Mr Giles and John Teather, a BBC executive, had created a climate of fear at the BBC Weather Centre through criticism and biting memos.
During the investigation Ian McCaskill, the forecaster, who is now retired, accused the two of acting "like prefects at a minor public school".
Mr Edgar's union representative reacted angrily to the appeal decision. "On behalf of Richard, I am surprised and indeed very disappointed with the decision of [Peter Ewins, the chief executive of the Met Office] to overturn the decision of his staff," said Elenor Hutcheson of the IPMS.
"It shows total disregard for the judgement of those staff involved in the procedure, who after a full investigation lasting many months, found Bill Giles guilty of serious misconduct," she added.
A spokesman for the Met Office said: "The Met Office has completed its investigation into the allegations of deliberate harassment and bullying made by Richard Edgar against Bill Giles, its senior weatherman at the BBC Weather Centre.
"Bill, who reached the normal Civil Service retiring age of 60 last week, has been cleared of the charges which would have amounted to serious misconduct.
"Nevertheless, in conducting a full and thorough analysis of the case, Peter Ewins has concluded that there are problems with management of the Met Office's activities at the Weather Centre and that changes are necessary."
The spokesman later said that the Met Office will be holding meetings with Mr Edgar and Mr Lee to discuss their return to work.