The BBC world affairs editor will take the pair to an as yet undecided destination, as he files reports for either Newsnight or the 10 O'Clock News.
In return, the explorers will lead Simpson on the type of trips they are more familiar with, to hone the broadcaster's adventure skills.
Sir Ranulph, whose records have included making the first surface journey around the world's polar axis, will guide the others on a week-long journey to the Arctic Circle in temperatures as low as minus 50C.
Sir Robin, the first person to sail single-handedly and non-stop around the world, will guide the voyage around South America's dangerous Cape Horn.
Sir Ranulph was forced to abandon his second attempt to conquer Mount Everest after succumbing to exhaustion in May.
The adventurer, who had a triple heart bypass operation in 2003 and has been in remission for prostate cancer, suffered heart problems and vertigo.
The BBC2 series, Three Dogs, will be broadcast next year.
Copyright Speakers Corner 2016