The 36-year-old has come in as a replacement for Petr Cech, who left the role this summer.
Vivell has previously worked as head of recruitment and scouting at Austrian side Red Bull Salzburg and Germany's Red Bull Leipzig.
Vivell's arrival is the latest move by Chelsea chairman Todd Boehly to put together a transfer committee, with Joe Shields and Laurence Stewart also arriving at the club.
Vivell's track record includes playing key roles in the signings of Erling Haaland and Josko Gvardiol for Salzburg and Leipzig respectively.
Boehly said: "We are delighted that Christopher is taking up this important leadership role at the club.
"His work in Germany and Austria speaks for itself. We are confident he will continue on his impressive trajectory here at Chelsea.
"He will provide important support to Graham and the ownership group and play a vital part in advancing our overall vision for the club."
Vivell added: "Chelsea are building the most exciting project in global football and I'm extremely proud to be joining the club.
"There is so much potential for the club to continue to succeed, develop and grow.
"Under the new ownership, Graham Potter and the broader sporting team, there is a clear and sustainable philosophy underpinned by performance analysis, data and innovation, and I am looking forward to playing a part in that."
