During his time at the airport Rudd has overseen the sale of a number of airports, including Gatwick, and a regrouping of the company to focus solely on Heathrow.
Heathrow is preparing to appoint a new chairperson who will continue with the airport’s expansion plans. Rudd will remain in post until the second half of 2016.
John Holland-Kaye, chief executive, said: "It has been an honour and great pleasure to work with Sir Nigel and I will miss his sound advice, unerring support and good humour.
"We are starting the process of finding a replacement for Sir Nigel and Heathrow thanks him for the tremendous work he has done for our company over the past decade."
Rudd said: "I’m really proud to have played a role in re-establishing Heathrow as a national asset for the UK. I’ve seen first-hand just how much of an economic engine Heathrow is for all parts of our great trading nation.
"That’s why it’s so important that Government lives up to its "open for business" mandate and expands Heathrow. We can keep Britain at the heart of the global economy and I will continue to actively make the case for a bigger and better Heathrow."