After his final match in charge, a 2-1 derby defeat by Cinderford Town at the weekend, his Chairman Steve Abbley thanked Adi for his efforts over the 16 months he was at the helm and wished him every success.
In an official club statement, Viveash said: "It is with mixed emotions that I am resigning from my post as Cirencester Town team manager to take up a coaching role in Chelsea Football Club's Academy.
"I would like to thank the chairman Steve Abbley for his belief in me and for giving me my first managerial post and my assistant Paul Hunt for his hard work and loyalty.
"I'd also like to thank the hard working behind the scenes staff who are the heartbeat of the club and have helped me enormously over the past 16 months, and the supporters for the continued support and most importantly the players for their hard work, application and attitude during my managerial post.
"I wish Cirencester Town all the best for the rest if the season which hopefully results in promotion and for the future.
"It is a wonderful club with superb facilities and I've been proud to manage the club."