Hammond was instrumental in hiring manager Alan Pardew, who was fired earlier this month with the club lying bottom of the table, 10 points below 17th-placed Crystal Palace with five league games left to play.
"We would like to place on record our gratitude for Nick's efforts during his two years in the role and wish him every success for his future," chief executive officer Mark Jenkins said on West Brom's website https://www.wba.co.uk.
Hammond was previously director of football at Reading, where he worked with Pardew until the manager left in 2003.
"West Bromwich Albion are a great football club which I was honoured to be a part of, great people, great supporters. I wish them every success going forward as I move on to future projects," Hammond said.
Terraneo, who was the sporting director with Turkish side Fenerbahce in his most recent role, will help in the recruitment of West Brom's new head coach and restructure the squad.
"In the event of our losing Premier League status, it will be a squad we will want to compete strongly for promotion back to the top tier," Jenkins added.
"Giuliano will assist in the recruitment long-term of a new sporting and technical director and he will also be involved in the complete review of the recruitment department."
West Brom also sacked chairman John Williams and chief executive Martin Goodman in February following the club's dismal performances this campaign.
(Reporting by Aditi Prakash in Bengaluru, editing by Pritha Sarkar)
