Bilic paid the price for the Hammers terrible start to the season.
The 54-year-old Scot had been linked with his national team's job in the past, however, he will bring a wealth of Premier League experience, however, since he has had a mixed time at the helm.
Moyes, however, maintains there have been mitigating factors behind his recent lack of success in the dugout and is confident he can rebuild his reputation at the London Stadium.
"We need somebody with experience, knowledge of the Premier League and the players in it, and we believe David is the right man to turn things around and get the best out of the players at the club".
"I don't know any manager who hasn't gone through negative periods, especially in the game today". Everyone is entitled to that. "Yes, I think I do", Moyes told the club website.
Deadly church shooting in Texas
The teenaged daughter of the pastor of the Texan church where a gunman shot dead more than 20 people is among the dead. There are reports emerging from Texas of a mass shooting at the First Baptist Church in Sutherland Springs.
"I have only managed five clubs in my career. But I would certainly go and talk to them". The most recent one [at Sunderland] was the wrong choice by me.
"Hopefully I can show what I'm really about". "It's a big job we have in hand now but I'm sure with everybody together we can get the right results between now and the end of the season".
Asked for his direct message to West Ham fans, Moyes responded: "Support the players, support the staff".
Moyes has only been handed a six-month contract - but he insists that suits him fine.
A deal to that will last until the end of the campaign could prove to be beneficial to the Hammers, as the managers they previously reached out to did not want to break ties with their current clubs at the midway point, although it could be extended for a further two years should the Irons want to keep him.