The 19-year-old attacker has signed a deal with the Hammers until 2023.
“We wish Armstrong all the best for his future career,” Celtic posted on social media.
The Irishman played two first-team games, against Hibs and Livingston last season, after arriving from Arsenal in 2018.
“I feel very good to have signed,” Oko-Flex told West Ham TV. “It’s good to sign for a big club like West Ham United.
“I’m very excited to get started here. There are a lot of positives around West Ham and it’s just a great Club to be at right now.
“I know a lot of the boys here already. I trained with some of them when I was younger, and I’ve played against some of them as well, so it’s been good settling in and the coaches have welcomed me in very nicely as well.
“I want to thank God first and foremost, and my family and my team around me – without them, none of this would have been possible. I’m just grateful for the opportunity.”
He added: “I grew up admiring a few players: Ronaldinho, because he was just gifted; Brazilian Ronaldo, who, for a No9, had everything; and Jay-Jay Okocha, because my parents are originally from Nigeria, and he’s someone I grew up watching on YouTube – he did some crazy things back in the past!
“I like to be direct, take on players, and work hard for the team and myself as well. I just try and create as many goals as possible and help my team to win.”