The Norwegian has signed a five-year deal at the Olympic Stadium.
Nordtveit's free transfer from Borussia Monchengladbach was confirmed by the Hammers on Monday, following months of speculation.
Bilic admitted his interest in the Norway international in March, but said that many clubs were also keen as he approached the end of his deal.
But the Croatian, it would appear, has pulled out all the stops to lure Nordtveit to the Olympic Stadium on a five-year deal.
"Of course it’s a big part," Nordtveit told the club website when asked if Bilic had influenced his decision. "He took his time to meet me, talk with me and show me he was interested.
"What he has done at West Ham speaks for itself and I’m really looking forward to working under the boss."
Bilic led West Ham to their highest league finish in 14 years (seventh), despite Sunday's final-day defeat to Stoke City.
The 47-year-old has been able put his own creative stamp on the team, with summer signing Dimitri Payet taking most of the plaudits.
And Nordtveit says he is looking forward to featuring alongside the Frenchman.
"He is a fantastic player," the former Arsenal midfielder added. "He can do something different on the field and I’m really looking forward to meeting him and seeing his qualities."
Nordtveit's arrival in east London is expected to see Alex Song return to Barcelona at the end of his season-long loan deal this summer.