Mr Branson won pounds 100,000 damages last year over a bribe Mr Snowden allegedly offered him to withdraw his rival bid to run the National Lottery.
The American was seeking a retrial of the libel action in which Mr Branson sued him over his rejection of bribery allegations that the Virgin chief made on a BBC Panorama programme in 1995.
Mr Snowden was also refused a retrial of his own libel action against Mr Branson's claim that he was offered a bribe during lunch at his home in 1993. That case gave rise to the famous "loo note", a brief resume of the bribery attempt jotted down by Mr Branson while in the bathroom.
Neither Mr Branson nor Mr Snowden were in court yesterday. A spokesman for the American said he was "disappointed" by the decision. "In hindsight, I wish I had not accepted Mr Branson's invitation to lunch," Mr Snowden said in a statement.
After the hearing Mr Branson said: "I am very happy that the court has rejected Guy Snowden's appeal."
Mr Branson said the case showed the danger of allowing a profit-making lottery to be owned by companies that are its key suppliers.
"The prize was so great that Guy Snowden was prepared to go to extreme lengths to succeed," he said.