Mr Garden was the flight operations manager, chief pilot and aviation adviser for the South Georgia Heritage Trust, a private Scottish conservation organisation that ran the $20million project.
A team of helicopter pilots dropped bait laced with the anticoagulant poison brodifacoum over the island, targeting mostly rats, but also mice, in one area.
Mr Garden said a lot of New Zealanders were involved, including pilots and ground crew.
New Scientist and the British Press Association has reported more than 4600 detection devices - including chewsticks coated with peanut butter, tracking tunnels and camera traps, as well as three sniffer dogs - had been deployed to check for any surviving rodents.
Prof Mike Richardson, chairman of the project's steering committee, was reported as saying ''To the best of our knowledge this island is rodent-free for the first time in two and a-half centuries.''
Mr Garden has been involved with many offshore island rodent eradication programmes, beginning with Campbell Island, cleared of rats in 2001.
He is now looking forward to two eradication jobs next year - one of giant mice on Gough Island in the South Atlantic, the other of mice on Midway Atoll in the Pacific.
He said he would like to go back to South Georgia at some stage to see how the island had changed but was not sure if that would happen.
