The Mexico international signed for the Hammers on Monday in a £16m deal from Bayer Leverkusen.
Before joining the German outfit, Hernandez spent five years at United, including one season on loan at Real Madrid, and he arrives at West Ham having scored 98 goals during his time at Old Trafford and in the Bundesliga.
Bilic has expressed his joy in bringing the 29-year-old to the club, and has also revealed that he wanted to capture him when he left United.
"I am happy that the deal is complete as it's a great signing for us," the manager told West Ham's official website. "I spoke to him a couple of seasons ago when I joined West Ham, when he was at Manchester United and they wanted to sell him.
"I wanted him but then he opted for Leverkusen, but we have had a good relationship since then. So when the opportunity comes now after the season and I found out he could be available, then I called him and he was happy straight away.
"From two years ago until now we had the same conversation, so it helped, of course. There were a few other clubs interested but we are delighted he opted for us."
Hernandez could make his league debut for West Ham against his former club United on August 13.