The 26-year-old agreed terms with the Falcons in February, but cup commitments delayed the immediate completion of the transfer.
"I am delighted to be able to publicly welcome Adam to Kingston Park. He is a quality player and a solid acquisition to our midfield as we prepare for the end of season playoffs and the final push towards our ultimate goal of a return to the Premiership," Richards told the club's official website.
Meanwhile, Powell added: "I've had a great time at Saracens. I'm really excited by what is happening at Newcastle under Dean Richards. I can't wait to get started."
Powell could make his debut later this month.