Mr Pochuyev said Prof Sokolov - who has been receiving hospital treatment for hypothermia - may have been under stress. Police later found the body of his student in his apartment, Russian news reports said.
The police report reportedly says that he planned to commit suicide dressed as Napoleon following his murder of Anastasia.
Students at the university have since described Sokolov as a "freak", stating he would often do impression of Napoleon and would call his lover "Josephine".
"He has admitted his guilt", Sokolov's lawyer Alexander Pochuev told AFP, adding he regretted what he had done and was now cooperating.More news: Messi gives set-piece masterclass as Barca outclass Celta
Oleg Sokolov, an expert on Napoleon, was rescued from the Moyka River in St Petersburg in the early hours of Saturday morning along with the backpack.
Media reports said that Sokolov also beat up and threatened to kill another woman in 2008 but was never charged.
She was reportedly a co-author with Sokolov's of joint research on the French military rule of Napoleon Bonaparte.
His victim is reported to be Anastasia Yeshchenko, with whom Prof Sokolov had co-written a number of works.More news: Twitter reacts to LSU's first half of domination against Alabama
Investigators did not name the man but police speaking to AFP identified him as Sokolov.
He has worked as a technical adviser to European television broadcasters on films depicting the Napoleonic era, and he was made a knight of the Legion of Honour in France in 2003.
Sokolov was also a member of France's Institute of Social Science, Economics and Politics (ISSEP), but on Saturday the society announced in a statement that he had been stripped of his position on its scientific committee.
"We learn with horror. the atrocious crime of which Oleg Sokolov is guilty.", it said.More news: Detroit hosts Vegas after Fabbri’s 2-goal game
ISSEP was founded by Marion Marechal, the niece of Marine Le Pen, leader of the far-right National Rally party and a former deputy of the party.
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