Robertson will take over Smith's role on 1 June. The new head of public affairs will have responsibility for parliamentary, media and community relations as BAA Scotland plans to add a second runway at Edinburgh airport.
Smith said: 'We can't grow our business if the community does not allow us to.
We have to keep politicians, as community representatives, aware of what we're doing and make sure they trust us.'
Robertson said his replacement's main challenge would be to 'transform the community relations programme and build on the relations we have with government, business and stakeholders, going in with a fresh eye to develop business in a responsible way'.
Passenger numbers to and from Scotland are expected to double to at least 40 million a year by 2020.
BAA Scotland hopes to fill the vacant position within three months. Meanwhile Smith, 59, plans to set up a consultancy, Alastair Smith Communications, when he leaves on 27 June, offering lobbying, media relations, event organisation and internal comms services.