Lopetegui takes charge after David Moyes' end of season departure.
Sullivan said: I would like to welcome Julen to the Club and wish him every success in his new role.
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"We believe this appointment will ensure a strong opportunity to build on the positive progress made in recent seasons, helping the Club to move forward in the direction that aligns with our ambitions.
We have been working hard behind the scenes to continue shaping the right strategy for West Ham United's future, and we are looking forward to bringing Julen's coaching ability, experience and personality to the Club."