Mikhalchuk, reported missing on March 21, was earlier identified by her husband by her wedding ring. Her body was found in the River Spree in central Berlin on April 10.
"The DNA test proved the drowned woman is 52-year-old Anna Mikhalchuk," police spokesman Norbert Gunkel said. "No traces of violence were found on her body, and an autopsy showed she drowned in the river."
Commenting on media reports suggesting the artist's death could be linked to her activities in Russia, the police officer said there is not yet evidence of this.
"There are not sufficient grounds for this version of events," the police officer said, adding that toxicology tests were still to be carried out, and that a final conclusion would be made by prosecutors.
In Russia, Mikhalchuk, also known as Anna Alchuk, was charged with inciting religious hatred after taking part in a controversial art exhibition focusing on religion in 2003, but was acquitted in 2005.
Much of the artwork displayed at the 2003 Moscow exhibition entitled 'Caution, Religion! was vandalized during the show. These included a painting of Jesus Christ's face imposed on a Coca-Cola logo next to the words "This is My Blood".
The artist had lived in Berlin since November 2007 with her husband Mikhail Ryklin, a philosophy professor at Berlin's Humboldt University. Mikhalchuk also taught at the university.
