Airport chairman Peter Coman said Clarke was an excellent leader to take over.
"We have worked closely with Matt over the last 16 years as a senior executive in the Infratil group and we are highly confident that he brings the leadership skill and experience needed for the role.
"The Board has long regarded Matt as a top-tier candidate, capable of taking Wellington Airport to the next level."
Sanderson is stepping down after 10 years in the role and signalled to the airport's board his intention to do so several months ago.
Coman said Sanderson has been outstanding, leading many significant investments in the airport and delivering growth for private and community shareholders.
"I would like to thank Steve for his leadership and vision over this period, and particularly managing the Airport through the difficult Covid period."
Sanderson has overseen the domestic terminal extension, the airport's first hotel, rejuvenated terminal retail, a new multi-level carpark building, and designation for expansion to the east.
The last two years have brought a new series of challenges responding to Covid-19 and the impact on the travel and hospitality industry, he said.
"The team at Wellington Airport has done an amazing job keeping the Airport safe and fully operational through unprecedented times."