The 23-year-old had a spell with Red Star Belgrade earlier in his career before moving to the United States in 2022 and he arrives at Tannadice after spending part of last season on loan at Danish side Aalborg.
United manager Jim Goodwin told the club’s official website: “Richard possesses an ideal balance between technical ability and physicality, both qualities that will significantly improve our midfield.
“Despite his relative youth, he has varied experience across world football on three continents, something that illustrates versatility and courage to test himself in different environments.
“Getting him up to speed with the rest of the group is now of paramount importance to ensure he can make the positive impact we anticipate he will during his time at the club.”
Odada is excited about joining United as they prepare to return to the Scottish Premiership next weekend following last season’s Championship title success.
“It feels nice to be wearing this shirt, as soon as I heard there was interest at the end of the season I just said ‘make it happen’ to my agent,” he said.
“The demands placed on the team both by the fans and ourselves as players are exciting. It’s a mentality I’m happy to work with.
“I’m looking forward to working hard and giving my best for the club, fans and my team-mates. I’m here to push us on to achieve our goals for the season.”