The 37-year-old German had been heavily linked to the post since leaving RB Leipzig, and the final terms of his contract have now been agreed.
He will be one of two Technical Directors at the west London club, with Laurence Stewart having recently joined from AS Monaco.
In nearly two-and-a-half-years at Leipzig, Vivell was responsible for recruitment and scouting across all age groups, but also co-ordinated the overall strategy for squad building and recruitment among Red Bull’s wider football group.
He previously spent five years with sister club Red Bull Salzburg in Austria as head of scouting and recruitment and before that was first team scout at Hoffenheim.
Vivell said: "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."
Todd Boehly, Chelsea Chairman, and Behdad Eghbali, co-controlling Owner, added: "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."
Boehly has been building a high-profile recruitment department with Vivell and Stewart joined by Southampton's Joe Shields as Co-Director of Recruitment and Talent and Paul Winstanley from Brighton as Director of Global Talent and Transfers in recent months.
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