The 21-year-old has moved to Huish Park on a free transfer, having agreed an 18-month deal with the League Two side.
Donnellan spent the first half of this season on loan in League One with Walsall, for whom he made 11 appearances, including eight starts.
He did not make a first-team appearance for the Baggies, but did spend time on loan at Dagenham and Redbridge.
"Coming down from a division higher and with his international experience, Shaun is a fantastic addition to the squad and has a bright future," said Yeovil manager Darren Way.
"He's been playing with former Glover, Joe Edwards, so he'll have heard good things about the club and I look forward to working with him."