Gordon moved from Scotland to Sunderland in 2007 in a deal worth £9million and Wright had claimed that he acted as an agent in the deal.
A club spokesperson said on Hearts’ official website: “We were confident that there was no substance to the claims being made and that this was an opportunistic move on the part of the agent.
“The agent was neither acting for the player or the club at the time of the transfer and played no part in the player’s move to the English Premiership team.
“We have said before that we have a duty to defend the club against the actions of those who want to use Hearts for their own personal gain.
“It is a pity that a former player, someone who may be regarded a hero and patriot of the club, wanted to rip the club off in so shameful a manner.
“Such people may pretend to be club patriots and defenders but in reality all they want to do is destroy any positive development and set other fans and media against the strategy that we are implementing.
“Hearts is delighted to have achieved this victory against a carefully planned action and we will continue to ensure that the club does not allow itself to be the victim of such unwarranted actions.”