He'll join the club on a transfer deal with Traktor Chelyabinsk - the KHL team that currently owns his rights.
Voynov left the Kings and returned to Russia last month to avoid deportation as a result of criminal domestic violence charges. He was arrested and served a jail sentence for harming his wife last October.
His contract with the Kings was terminated when he returned to Russia.
SKA St. Petersburg employs former NHLers Ilya Kovalchuk and Alexei Ponikarovsky.