The Hammers paid Eintracht Frankfurt £45m to sign the French striker, who has signed a five-year deal worth around £70,000-a-week.
Husillos said: “The signing of Sebastien is a big investment and another clear signal of our ambition and desire to bring success to West Ham United and our supporters, and we look forward to seeing the big contribution he will make in the coming seasons.
“It is no secret that we have been in the process of identifying a top-class striker to add to the squad this summer, and much work has gone on behind the scenes to ensure that we were in a position to act once the right opportunity became available.
“Sebastien is a player we have been watching closely for some time - he has always been a key target and someone who myself, [manager] Manuel Pellegrini and [co-owner] David Sullivan were very keen to bring to the football club.
“He is a player with excellent pedigree and experience in three of Europe's top leagues. His record at Eintracht Frankfurt in recent seasons has been up there with the top strikers in the Bundesliga, and we believe that his physical and technical qualities will be well suited to the Premier League."