A well-known Russian professor and Napoleon expert was found by Russian police in the Moika river in St. Petersberg on Saturday.
Police reportedly then went to Sokolov's dwelling the place they found the decapitated physique of Anastasia Yeshchenko, 24, with whom he had co-authored quite a lot of works.
Lawyer Alexander Pochuev said Sokolov has signed a statement of guilt, the Russian media reports said.
Mr Pochuyev said Prof Sokolov - who has been receiving hospital treatment for hypothermia - may have been under stress.
Speaking on condition of anonymity, he said Sokolov was dedicated to his work but was also emotionally unstable and abused alcohol.
Anastasia had been in a relationship with the historian, 63, when he "accidentally killed her" following an argument, according to the report which stated he had confessed to police.
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".
The historian, who obtained France's Legion of Honneur in 2003, is the writer of books on French statesman and navy chief Napoleon Bonaparte and had acted as a historic marketing consultant on a number of movies.More news: Overwatch 1 and 2 players will play "side by side"
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Investigators opened a criminal case after the man was pulled out of the Moika River, a waterway in the heart of the historic city, early Saturday morning (local time).
Many expressed dismay, saying Sokolov had always been known for his hostile behaviour but officials had ignored complaints.
Both he and his lover studied French history and liked to wear period costumes, with Sokolov dressing up as Napoleon. Local media reported that he was drunk when he was found.
Sokolov was president of the Russian Association of Military History and is now a member of the body's scientific council.
The scholar was a member of France's Institute of Social Science, Economics and Politics, which removed him from leadership role in response to the killing, according to AFP.
"We learn with horror about the atrocious crime of which Oleg Sokolov is allegedly guilty", it said in a statement on Twitter.
ISSEP was founded by Marion Marechal, the niece of Marine Le Pen, leader of the far-right National Rally party.