The moves follow BA's £4.4bn merger with Iberia this week to form International Airlines Group (IAG).
BA has hired Frank van der Post as managing director, brands and customer experience. A spokeswoman said his role would not cover the Iberia brand.
Crawley has been promoted to commercial director for IAG. He will join IAG’s board in January and will have "particular responsibility for exploiting the revenue opportunities", which come from the merger.
Van der Post is currently chief operating officer at Jumeirah Group and previously worked at Intercontinental Hotels.
Post’s arrival will coincide with IAG's appearance on the stock exchange next year, expected on 24 January.
Crawley is one of the four current and former British Airways executives acquitted of price fixing in May this year.
The case, in which BA was accused of conspiring with rival Virgin Atlantic to price fix fuel surcharges, collapsed after a series of emails sent and received by former Virgin Atlantic communications director Paul Moore came to light.