The Hammers finalised the £16m capture of the former Manchester United star from Bayer Leverkusen on Monday.
"We are delighted to welcome Javier as the latest fantastic addition to the West Ham United squad," Sullivan told the club's official website.
"Following the arrivals of Pablo Zabaleta, Joe Hart and Marko Arnautovic, he is another top-class professional who brings great experience and quality to the club.
"He has a proven goalscoring record in the Premier League, La Liga and the Bundesliga, as well in the UEFA Champions League and at international level with Mexico.
"We now have some fantastic options in attacking positions and, like all West Ham fans, I am looking forward to seeing Javier score goals in a claret and blue shirt next season."
Hernandez scored 39 goals in 76 games for Leverkusen across a two-year spell.