Shrews reached a settlement with the winger to bring an end to his contract one year early.
Town boss Paul Simpson told the club's official website: "Marc and I had a chat at the end of last season where I explained my plans to him.
"We both felt that it was in our best interests that he moved on.
"We have reached an agreement on compensation and the savings made by doing this will be ploughed straight back into strengthening the squad further."
Pugh made a £50,000 move from Shakers in 2007 and played 45 times for Town, scoring four goals, but he struggled to get into the side last season and went on loan to Luton and Hereford.