Helicopters helped lay rat bait over 1087 sq km (108,723 hectares) of the south Atlantic island in three phases, beginning in 2011.
Three rodent detection dogs scoured 2420km this winter to sniff out any sign of the rats – but none were found.
The dogs’ two handlers – part of ‘Team Rat’ – also climbed the equivalent ascent of Mount Everest eight times over.
More than 4,600 rat chewsticks and tracking tunnels were laid on and checked as part of the survey on the 103 mile-long island – which lies some 800 miles south of the Falklands and is a British Overseas Territory.
The rats – which stowed away on whaling ships in the 18th century – had had a “devastating” effect on the island’s birds, forcing them onto smaller offshore islands.
Two species found nowhere else on Earth were particularly at risk – the South Georgia pipit and the South Georgia pintail.
The sub-Antarctic island’s huge king penguin colony – said to be the world’s largest – also featured in the BBC’s latest Blue Planet series.
The £10m rat project was run by Scottish-based charity the South Georgia Heritage Trust and its US counterpart, the Friends of South Georgia.
Its Habitat Restoration Project was eight times bigger than any other rodent eradication area.
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“Thanks to the outstanding work of the passionate and committed members of Team Rat and the Board of Trustees, the birds of South Georgia are free from the threat of rodents,” said Professor Mike Richardson, Chairman of the SGHT Habitat Restoration Project Steering Committee.
“The trust can now turn its attention and efforts to working with the Government of South Georgia & the South Sandwich Islands on conservation of a different kind: the conservation and reinterpretation of the island’s historic cultural heritage to educate and enlighten future generations about our environment.”