The 22-year-old underwent the operation in Leeds on Wednesday and is expected to miss the rest of the season.
Speaking at Springfields on Thursday morning, Neil said: "Josh went for his operation on Wednesday and he is back in with us next Monday.
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"It was a routine operation really, obviously a success and he'll get his rehab started as soon as he can."
Harrop tore the anterior cruciate ligament in the 3-2 defeat to WBA on September 29 , it occurring as he helped set-up North End's second goal in stoppage-time.
Neil said: "With an ACL injury, you get ones which you operate on and ones which you don't.
"Although if you have the operation you will be out a bit longer, at least you are going in and seeing the source of the problem.
"When it is an injury where it's a strained ACL for example, those ones are a 'how long is a piece of string' type in terms of when you get back.
"It is a case of how much the body can cope with, how quickly it heals itself, will you need an operation three months down the line, that kind of thing.
"From our point of view although Josh is probably going to miss the rest of the season which is disappointing for him and for us, at least we know the extent the injury and we can draw a line under it.
"We have a focus point for him to come back."