It also ruled that Mr Stewart had intended to "tarnish and damage" that name.
Mr Stewart, of Gourock in Scotland, claimed he had a right to register the site to advertise the mating services of his dog Rougemar Billyconnolly.
However, the WIPO agreed with the comedian that he had common law rights to a name established over a 30-year career.
It also ruled that Mr Stewart had intended to "tarnish and damage" that name.
'Bad faith'
Connolly, 58, claimed Mr Stewart originally offered to hand over the domain name in return for a five-year supply of his Tickety-Boo Tea and a press announcement about the agreement.
Connolly said that Mr Stewart rejected an offer of £202.80 - the commercial cost of the tea bags.
Connolly also claimed he offered Mr Stewart £750 for the name, but that Stewart upped the price to £7,500, plus legal expenses.
A message on the dog's website claimed to have as much right to the site as the comedian.
"I know it's a dog's life but is there no justice in this world?," it read.
"Dogs have as much of a right to advertise their services on the World Wide Web as banjo-playing ex-shipyard welders," it said, referring to the Glaswegian comedian's early working years in his hometown.
However, WIPO panellist David Perkins rejected Mr Stewart's right of ownership.
He dismissed the claim that the website could be named for the dog, especially as the dog had been called Rougemar Pindar to begin with.
Mr Perkins also ruled that Stewart was using the name in bad faith and was in the business of buying and selling celebrity domain names.
Anyone can register a domain name for a few dollars, which has led so-called "cybersquatters" registering famous names in order to sell them back for a large sum.
Connolly is the latest of a number of celebrities from around the world who have taken similar action over the use of their name on the internet.
Hollywood actress Julia Roberts and pop star Madonna are two who, like Connolly, have won their cases.
Others such as the singer Sting, however, have been overruled.