The move is part of a raft of leadership changes which also sees Keith Williams, who had led the company as executive chairman since May, move into a non-executive role.
Royal Mail said Martin Seidenberg, chief executive of logistics firm GLS, will join the board from April.
Mr Thompson said: “Against the backdrop of a challenging year, our colleagues have once again demonstrated the invaluable service they provide for our communities up and down the country.
“Looking ahead, we need to build on the great trust we have on the doorstep. We need to develop a razor-sharp focus on the customer, making sure our services are delivering exactly what our customers need and want. And we need to explore new opportunities for growth.