It includes Suzanne Roddie, who has been promoted to chief operating officer, and Juha Jaervinen, who succeeds Koster as Virgin's chief customer officer.
Other key appointments include Beck Woodmansee as chief people officer, Dave Geer as chief commercial officer, Ansar Hussain as chief financial officer (interim) and Holly Boyd-Boland as senior vice-president corporate development and legal affairs.
Recruitment is also under way for the role of chief digital and information officer, who will be tasked with marrying Virgin's efforts across technology, digital development, data, artificial intelligence and transformation.
It was announced in October that Weiss, who joined Virgin Atlantic in 2014 and took up the top role with the carrier in January 2019, would be succeeded by Koster.
“I’m incredibly proud and energised to be leading Virgin Atlantic into its next chapter," said Koster. "This airline has always been defined by its people — their red spirit, professionalism and unwavering care for our customers and for one another.
"I’m confident this leadership team brings together the experience, leadership qualities, innovative thinking and collaborative mindset needed to build a strong and exciting future for the airline we all love."