But last week the High Court in Wellington decided there were no grounds for granting an interim injunction on physical works before the judicial review case was heard.
Clarke said he still thought an overpass would have been a better and safer solution, which was supported by Wellingtonians and businesses.
"We want to work constructively with Let's Get Wellington Moving as they develop plans for mass rapid transit and other key projects. Our hope is that the views of local residents and the business community will be listened to carefully."
Clarke said there was a strong shared interest in improving Wellington's transport network to create a more liveable and sustainable city.
Waka Kotahi systems design regional manager Kesh Keshaboina welcomed the airport's decision.
"We're now looking forward to delivering a signalised crossing that keeps people safe when crossing Cobham Drive.
"This will be a great step towards encouraging people to choose different ways to travel, which is one of the top priorities of the Let's Get Wellington Moving programme."