Polglass has been promoted from managing director of the TNT Post London division.
Neilson, who has been with TNT Post UK for 17 years and became commercial director in 2008, will spearhead the company's infrastructure planning in the new role.
TNT did not give much more detail, saying only that it was examining the supply chain and reviewing its options.
While it has developed as a credible competitor to Royal Mail in direct mail collection and distribution, it still has to use the state-owned operator's "last-mile" resource of postmen and women.
Nick Wells, chief executive of TNT Post UK, said: "Charles will develop our infrastructure to meet the high demand for our services in the UK, and Nigel has a proven understanding of our customer proposition and the needs of the postal market, where we will continue to innovate and provide new services."