The Reds assistant head coach worked successfully alongside Ismael during his time at Oakwell in 2020-21, with the Frenchman subsequently expressing a desire for Murray to join his staff after making the switch to the Midlands last week.
Head of sports science Jonny Northeast has also moved to Albion alongside analyst Jack Riley, while former Reds head coach has secured the signature of Reds captain Alex Mowatt on a three-year deal.
A Barnsley statement confirming the exit of Murray, Northeast and Riley read: "Adam Murray has left his role as assistant coach at Oakwell to take a position at West Bromwich Albion.
"Head of sports science Jonny Northeast and analyst Jack Riley also leave for the Hawthorns.
"The club would like to take this opportunity to thank the trio for their work and wish them luck for the future.
"All compensation received from the buyout of these contracts will be reinvested into the first team squad ahead of the approaching season.
"Further updates regarding Marks Schopp's new backroom team will follow in due course."
The club has since appointed Matt Cook, a former Head of Medicine and Science at Manchester City, to replaced the highly-regarded Northeast.
Birmingham-born Murray - who turns 40 in September - had two caretaker spells in charge of Barnsley, encompassing eight matches in the autumn of 2020 and 2019.
They included a 2-2 draw at West Brom in October, 2019.
He was interviewed for the full-time position last October alongside Ismael and ex-Brondby and Leipzig head coach Alexander Zorniger.
Murray combined the roles of captain and assistant manager when Mansfield Town won promotion to the Football League in 2013 – ahead of becoming the youngest manager in the league when he was handed the reins at Field Mill at the age of just 33 the following year.
He was sacked just under two years later before a spell as manager at Boston United, which was followed by a short stint as assistant at non-league Guiseley.
Murray joined Barnsley as under-18 coach in 2018 and was later handed more responsibilities with the first team by Daniel Stendel.
On completing the signing of Mowatt, Ismael said: “Last year Alex put his performances on the next level.
“He is an outstanding midfield player with outstanding qualities and mentality. He scores goals outside the box and on set-pieces he is very dangerous.
“He is a hard worker with the right mentality and a lot of energy. The way Alex plays will suit the West Brom mentality.
“He is a leader as well. He is still a young guy but he has a lot of experience. He has hunger and he is the exact profile of player that suits West Bromwich Albion. Alex is the first signing and the first step.
“Signing Alex is important to help the team understand the principles of our play. It will give the guys more confidence and understanding of how we want to play. It will be easier for them to follow him.
“He is a hard worker with the right mentality and a lot of energy. The way Alex plays will suit the West Brom mentality."