Edinburgh fighter Arthur was already 'interim' champion as he awaited his shot at outright champion Joan Guzman but has been denied the chance to win the belt inside the ring after the Dominican Republican fighter decided to move up to the lightweight division.
The 29-year-old Scot had been set to face the fearsome puncher known as 'the Little Tyson' in the capital on May 3 but Guzman failed to secure a visa in time. A new date had been anticipated before Guzman's decision to let the title go and move on.
Promoter Frank Warren revealed the search is under way to find a replacement opponent for what will be Arthur's first defence this summer.
And Arthur, who became interim champion with last summer's victory over Koba Gogoladze, is keen to return to action.
He said: "I'm delighted with the decision by the WBO to give me full world champion status but I felt I won the title when I beat Koba Gogoladze last July.
"I'm confident I would have beaten Guzman had the fight been rescheduled but I believe that I'm among the elite super-featherweights and want to prove myself as the best out there.
"But 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."
Sports Network chief Warren said: "Britain has lost a few of its world champions over the last few months but we have got one back with Alex now declared as world champion.
"I believe he will be a long-term world champion.
"I'm working hard at the moment to deliver a new date and challenger for Alex."
Guzman, meanwhile, moves into a talented lightweight division featuring the likes of Manny Pacquiao, Juan Manuel Marquez, David Diaz, Nate Campbell and Joel Casamayor.
A showdown with IBF, WBO and WBA champion Campbell - touted as a future Amir Khan opponent - could be Guzman's first fight in the 135lb division.