Speaking on Radio 2 on Thursday morning, Mills said he felt “a bit sad it’s all done now”.
He added that it “really felt like anyone could have won” as there were just 39 minutes between all the teams when they started the final leg.
Despite starting the last leg in third place, the couple tossed a coin to determine which route they would take from Tilcara to Frutillar.
They decided to travel through Argentina to San Salvador and onwards to Mendoza.
After opening the guest book to discover they were the winners, the pair jumped up and down shouting “oh my God, we did it”, before embracing each other, overcome with emotion.
In an interview reflecting on the journey that took him 12,500km across south America, Mills said: “When we were on the top of the volcano, we had a hug and a little cry.
“People were telling us repeatedly that we had won, but I still could not compute it. I could not get it in my head.”
The DJ said he had assumed they were the last to reach the checkpoint.
“I do actually remember saying to him, ‘There’s no point in running, Sam, we’ve lost.”