The body of the 22-year-old was discovered in a remote wood near the A83 west of Arrochar by a passer-by last Thursday.
Ms Solodyankina, who was studying physics at Edinburgh University, was reported missing on 12 June last year, sparking a nationwide missing persons hunt.
Police last night confirmed the remains were the student’s and said her parents, who live in Moscow, have been informed. There are no suspicious circumstances concerning her death, they said.
A spokesman for the Find Yulia campaign, set up after she vanished, said: “No words can express the sadness we feel regarding the death of our friend Yulia.
“We feel blessed to have spent the time that we did with her.
“Yulia was full of energy, a beautiful dancer, caring friend and a kind and gentle soul. Our thoughts go out to her family and loved ones.
“We would like to thank the thousands of people involved in the Find Yulia campaign. We feel overwhelmed by the number of people who offered their support and sent kind words.
“It has been heartening to realise how many people really care. We would encourage anyone struggling or feeling a sense of desperation to reach out for help and support.
He added: “We miss Yulia so much and will never forget her.”
Last night her friend Washu McWatt said: “I wish I saw Yulia in Glasgow that day, I would have spoken to her and told her how beautiful and intelligent she was and no degree would need to prove it.”
Members of the Find Yulia campaign had complained about the time it was taking police to formally to identify the remains after they were found.
Police sources had revealed they had faced considerable difficulty obtaining a reliable sample of Yulia’s DNA which they could match to the badly decomposed remains.
Ms Solodyankina, originally from Moscow, disappeared after learning she had failed her fourth and final year.
And at the time of her disappearance her boyfriend, Antoine Dao, described her as feeling “very stressed” after her final exams.
The Russian had not been in contact with friends or family since 6 June after leaving a bar in the centre of Edinburgh at around 9pm.
The last recorded sighting was captured on CCTV at Buchanan Street bus station in Glasgow at 4:55pm on 7 June.
Due to the location of the discovery, there had been some speculation the body was that of missing Edinburgh bookkeeper Suzanne Pilley, who disappeared in May 2010.
Ms Pilley’s former boyfriend, David Gilroy, 50, was convicted of her murder and jailed for life. Her body has never been found, and prosecutors believe Gilroy dumped it in that area of Argyll.