Yuri Possokhov was born in the city of Lugansk, Ukraine. After graduation from the Moscow Choreography College (today the Moscow State Academy of Choreography) in 1982 joined the ballet troupe of the Bolshoi Theater.

Throughout 10 years his repertoire included the main parts in Pyotr Tchaikovsky's ballets The Swan Lake, Sleeping Beauty and The Nutcracker, as well as the leads in Chopiniana, Sirano de Bergerac, Romeo and Juliette, and others.
He became the first performer to play the title part in George Balanchine's first ballet staged in the Bolshoi Theater - it was The Prodigal Son by Sergey Prokofiev.

In 1992 Yuri Possokhov signed a contract with the Royal Danish Ballet, and then was invited to perform the part of Prince Désiré in The Sleeping Beauty staged by Helge Tomasson, with the troupe of San Francisco Ballet. Since 1994 he has been the principal dancer of this company. In 1999 Yuri Posokhov organized a Russian tour of some of the troupe's dancers under the name Ballet without Borders.

Since the late 1990s Yuri Possokhov has been actively working as a choreographer. The most famous of his works are as follows: Spanish Songs (1997, for the San Francisco Ballet prima ballerina Muriel Maffre); The Duet for Two (1997, for Joanna Berman); Impromptu set to A. Scriabin's music (1997, for Felipe Díaz), and others.

In 2002 Yuri Possokhov staged the ballet The Cursed based on Euripedes' tragedy Medea. In 2003 he co-staged the full-length ballet Don Quixote jointly with Helgi Tomasson, the director of San Francisco Ballet.

Magrittomania created by him in the framework of the San Francisco Ballet's project Discoveries (2000), gained Yuri Possokhov the Isadora Duncan Award.

In 2006 he staged his own version of S. Prokofiev's ballet Cinderella in the Bolshoi Theater.

The year 2012 saw the premiere of his Classical Symphony with San Francisco Ballet in the Bolshoi Theater. It was followed with a number of this ballet stage productions in the National Romanian Ballet, the Cincinnati Ballet  and the Atlanta Ballet in 2015.