International Airlines Group (IAG), which owns both airlines, also announced IAG Cargo chief executive Steve Gunning as the new chief financial officer at British Airways.
He replaces Nick Swift who is leaving the airline, having spent five years in that role.
IAG said announcements about the new chairman and chief executive of Vueling and new chief executive of IAG Cargo would be made in due course.
Commenting on the new appointments, IAG chief executive Willie Walsh said: “Under Alex Cruz’s leadership, Vueling has become a dynamic, innovative and cost-effective airline and Alex will bring new experience and insight to British Airways.
“Steve Gunning will return to British Airways to support Alex as chief financial officer. He has been highly effective in setting up IAG’s first ever single business unit at IAG Cargo. The business is industry-leading with a ground-breaking operating model and cost focus.”