The 19-year-old midfielder, who made his international debut for Wales on Thursday, has left United for the first-time.
He made his first-team debut in the Europa League last year and will be looking to build some experience at the Valley under Lee Bowyer.
On joining the Addicks, Levitt told the club's website: “It feels amazing obviously. It's a big club, even though we are in League One, it's still a massive club, so it's a pleasure to be here.
“I've spoken to Lee a few times now, he's looking to be the best this season and get back into the Championship where Charlton belong."
Our new number @DylanLevitt#cafcpic.twitter.com/UC5ghtrGFx
— Charlton Athletic FC (@CAFCofficial) September 8, 2020