The 18-year-old thanked Tutberidze for training her for more than a decade in a statement published by the Russian Figure Skating Federation.
"I will continue to compete for the Russian Federation... but I will train under Canadian specialist Brian Orser," Medvedeva said.
"I am doing this to use new possibilities and other training methods and continue to represent Russia at the highest level."
Medvedeva, twice world champion, was upstaged in Pyeongchang by her 15-year-old training partner Alina Zagitova, finishing 1.31 points behind her in the women's singles competition.
Orser, twice Olympic silver medallist, coaches some of the world's leading figure skaters, including Japan's double Olympic men's champion Yuzuru Hanyu.
(Reporting by Gabrielle Tetrault-Farber, editing by Ed Osmond)
