"I'm confident that I would have beaten Guzman had the fight been rescheduled but I believe that I am among the elite super-featherweights and want to prove myself as the best out there.
"I'm proud to be Edinburgh's first world champion for 30 years, and am looking forward to making the first defence of my title. My reign begins now."
Promoter Frank Warren said he expected Arthur to be a "long-term world champion".
He added: "I'm working hard at the moment to deliver a new date and challenger for Alex."
When Arthur was named the WBO's interim champion it effectively meant he was considered the organisation's number one contender.