Weiss, who has headed up the airline for the past seven years, will be succeeded by chief customer and operating officer Corneel Koster.
Koster rejoined Virgin Atlantic in 2019, and is credited with leading on the introduction of the carrier's new A330neo aircraft and delivery of its digital operational transformation.
During a career spanning three decades, Koster has head senior operational and commercial roles at Virgin Atlantic partners Delta Air Lines, Aeromexico and KLM.
Between 2010 and 2013, Koster was Virgin Atlantic's director of operations, safety and security.
Weiss, meanwhile, joined Virgin Atlantic as chief financial officer in 2014 and progressed to the role of chief commercial officer before becoming chief executive in January 2019.
Besides steering the carrier through the pandemic, he oversaw Virgin's subsequent return to profitability, and strengthened both the airline's customer satisfaction record and its credentials as a good workplace.
Sir Richard Branson, Virgin Atlantic's founder, paid tribute to Weiss. "Shai has done an outstanding job over the past seven years," he said.
"I’m grateful for his vision, passion and commitment to creating brilliant experiences that have made the airline stronger and raised the bar across the industry."
Branson added Weiss's successor, Koster, "embodied the Virgin spirit". "We look forward to this exciting new chapter," he added.
Virgin Atlantic chair Peter Norris said Weiss had endured "exceptional headwinds" during his tenure. "While we’re sad he’s decided to stand down, he has done an excellent job leading from the front in service of our people, customers and the communities in which we operate, setting Virgin Atlantic on a clear path towards future success."
Like Branson, Norris praised Koster's leadership credentials. "As a true customer champion, he understands what sets Virgin Atlantic apart as we continue to challenge the status quo in the years ahead.
“We thank Shai for his contribution and leadership, and we wish Corneel and the team every success in this next exciting phase.”
Weiss said: "I can think of no one better to take over as he [Koster] knows what it takes to drive Virgin Atlantic to the next level and he’ll continue to innovate for our people and our guests, making them smile every step of the way.
"I leave Virgin Atlantic full of pride, knowing I have played a part in its bright red history. Together, we’ve transformed through the pandemic and emerged faster, better and stronger than ever."
Koster added: "It’s an incredible privilege to take up the role of chief. We’ve always done everything in our power to give our customers and our people the best experience in the skies.
“I’d like to thank the Virgin Atlantic Board for their trust and confidence and to thank Shai for his leadership and his friendship. I’m proud to lead our talented teams into our next chapter."
