Shaymen boss Chris Wilder moved to snap up the goalkeeper, who was brought through the ranks at Liverpool.
"We have had to remain patient with this one because he wanted to come but he had to sort out a few things with Shrewsbury first," Wilder told the club's official website.
"While he has plenty of experience in the league, he is not coming to the end of his career."
Dunbavin played over 100 times for Shrewsbury after joining them in 2000.
