The German authorities moved ahead of a summit on Ukraine to be attended by Russian President Vladimir Putin and German Chancellor Angela Merkel, along with French President Emmanuel Macron, in Paris on Monday.
The foreign ministry in Moscow said it would be forced to respond with retaliatory measures.
"He was carrying a Russian passport which identified him as Vadim Sokolov, but German prosecutors on Wednesday confirmed that they now believe that is a false identity", the Telegraph says, adding that police findings indicate that it is "highly likely" the arrested man is Vadim Krasikov, a Russian national previously wanted for the murder of a businessman in Moscow in 2013.
He survived a 2015 assassination attempt, despite being shot four times, and later fled to Germany.
The German investigation is also looking into a possible link to officials in Chechnya, a republic within the Russian Federation that has its own constitution but is still controlled by Moscow.
Russian Federation has denied any involvement and said on Wednesday it would retaliate for what it called Germany's "unfriendly" move.
Khangoshvili fought against the Russians during the Second Chechen War from 1999 to 2009, and worked thereafter in both Georgia and Ukraine against Russian interests, according to Deutsche Welle.
Federal prosecutors in Germany take over investigations when there is a strong suspicion of involvement by a foreign state.
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Berlin prosecutors named the victim, who was shot in the head in a central Berlin park, only as "Tornike K".
The German Foreign Ministry announced the expulsion of two employees of the Russian Embassy in Berlin earlier on Wednesday, after Russian authorities didn't answer requests by Germany to help shed light on the killing of the 40-year-old man. It did not identify the names or the functions of the two diplomats being expelled.
Investigators found that Zao Rust had only one employee in 2018 and on April 10, 2019, was listed as being in "reorganization".
Vadim S is then said to have flown to Warsaw where he stayed in a hotel until 22 August.
But the company was not operational and a fax number for the firm was registered to another company belonging to Russia's defence ministry.
It is not clear, they said, what he did between his departure from the hotel and the killing at 11:55 a.m. on August 23 in Berlin.
Previous year they expelled 100 Russian diplomats over the Skripal poisoning. Moscow has denied any involvement in the case.
After that attack, Western nations banded together to expel more than 100 Russian diplomats they accused of being spies, including 60 from the U.S.