The Wales international had been struggling with a shoulder problem for several months and finally made the decision to rule himself out of the rest of the season in order to hit the ground running for the 2013-14 campaign.
The operation took place on Thursday morning and, according to head of performance Glen Driscoll, was a complete success.
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"It's going to be a relief for Joe that this has now happened for him. It has been quite a long-standing issue. He was repetitively subluxing, so his shoulder was coming out very easily and very often.
"It was a procedure that was very important. He should be 12 weeks from now, so he'll be fighting fit for the start of pre-season."
Allen's performances have come in for some criticism in recent weeks but Driscoll believes that his shoulder condition must have played a considerable part in his disappointing form.
"I think he has done amazingly well," he continued. "Anyone who has ever had repetitive subluxations of shoulders will know there is a lot of apprehension involved.
"I find it difficult to see how that wouldn't have affected Joe. It was getting to the point where he would do a high-five to celebrate a goal and would actually feel a sublux.
"When you know this is happening, it's not just the pain that occurs - it's the apprehension.
"He has done very well to get through this and it's great for him that we can draw a line under this, get him fit and see how he goes next season."