In Islam dogs are regarded as unclean and are not allowed in mosques.
Guide Dogs for the Blind said it was "a massive step forward for other blind and partially-sighted Muslims".
"They were actually very good and they were the ones who were willing to help because they said it is their duty to accommodate.
"He does just lie down and relax there and sit here. Being a guide dog, their whole manner is to be calm and relaxed and just out of the way."
A special rest area has been set up in the entrance of the Bilal Jamia Mosque for Vargo to stay in while his owner is praying.
The decision was made after lengthy discussions with Muslim leaders"Mohammad Shahid Raza, director of the Imams and Mosques Council UK, said: "I believe that in all new mosques such facilities for disabled people will be an essential part of their design.
The Bilal Mosque is going to provide special provision for such guide dogs to be kept safely and securely within the mosque complex during such visits.