The London-based Young, 32, plans to run 314.4 miles between Sep 7 and Oct 1, and travel for 130 hours by plane as part of his endeavour. His final run will be at Newcastle upon Tyne in Britain Oct 1.
He will run another half-marathon in Mumbai Tuesday.
ICI Dulux, where Young works as a management consultant, is supporting the cost of his runs.
Sir Ranulph Fiennes, Lord Sebastian Coe, Paula Radcliffe and David Walliams are among the celebrities who have lent their support to his cause.
Young was diagnosed with thyroid cancer in 2003. He was treated with radioactive iodine and then had a surgery to remove the tumor from his thyroid.
But two years later, he was told that the ailment has recurred and he again underwent a surgery to remove his thyroid gland.