The British and Irish Lion, 33, has penned a three-year contract with the Aviva Premiership club.
"I have enjoyed eight fantastic seasons at Ulster and will leave the club with many happy memories," Court told London Irish's official website.
"London Irish is a new challenge and one I am looking forward to. There is still a lot of work to do for the remainder of this season at Ulster and that will be my immediate focus."
Court has won six caps for Ireland since making his debut in 2009.