Vivell earlier worked with RB Leipzig, where he was responsible for recruitment and scouting across all age groups in his native Germany.
Vivell, who also worked with Leipzig's sister club Salzburg, said Chelsea are building "the most exciting project in global football".
"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," he added.
Chelsea are eighth in the Premier League and host Bournemouth on Tuesday.