The 38-year-old won the 2010 race but was later suspended for 38 months.
The judgement to recover her appearance fees and prize money for the 2010 and 2011 races needs enforcing by Russia.
“Cheats should not benefit,” said London Marathon Events Ltd chief Nick Bitel. “It will be a long and difficult process but we will pursue it.”
Ethiopian Aselefech Mergia was named the winner of the 2010 London Marathon after Shobukhova was stripped of her win. The Russian was runner-up in 2011.
Bitel said any money returned by Shobukhova will be redistributed to athletes that were “cheated out of their rightful dues”.
Shobukhova also had her results from 2009 annulled and was also stripped of Chicago Marathon wins in 2009, 2010 and 2011.
Her ban was reduced by seven months, for assisting a World Anti-Doping Agency investigation.
Shobukhova is banned for life from taking part in the London Marathon and in any of the five other marathons that make up the World Marathon Majors.