The Frenchman, who took the Tykes to the Championship play-offs last season, has replaced Sam Allardyce in the Hawthorns hot-seat.
"I feel really proud to have accepted this challenge. I feel a big responsibility but I'm ready for this job and I am delighted to be here," Ismael told the club website.
"This was the next step I wanted to take in my career. Although there's going to be a lot of hard work this season, I am excited for the big task in front of us.
"It's a big commitment from the club to want me to implement a philosophy I want for the next four years. We have a clear plan and vision of where we want to go."