Ismael has signed a four-year deal with the Baggies after they agreed a £2m compensation package with the Reds, now looking for their sixth head coach in less than three-and-a-half years.
Barnsley have pledged that all proceeds of the buyout will be used to strengthen the squad.
Work permit rules following Brexit are likely to mean that appointing another head coach from Europe will not be straightforward following previous successful moves for Ismael, Gerhard Struber and Daniel Stendel.
Early domestic names in the betting include one-time Reds midfielder Alex Neil, ex-Aberdeen chief Derek McInnes and Rotherham United boss Paul Warne.
A Reds statement read: “Now continued progression must be ensured, with the recruitment process for a new head coach already under way.”
Ismael’s move comes at an uncertain time for Barnsley, with chief executive officer Dane Murphy wanted by Nottingham Forest. His deal runs out next week.
Captain Alex Mowatt whose contract also expires at the end of June, is also likely to be on the wanted list of Ismael.