The 28-year-old featured 19 times for the Falcons last season while dual-registered with Blaydon RFC.
Rogers moved to the National League One outfit from Lille after enrolling as a student at Northumbria University.
"With Alex studying at university and playing locally last season, it gave us a chance to keep an eye on and try out a player I knew from Harlequins and I thought he did well for us when he played," director of rugby Dean Richards told the club's official website.
"Coming into the side on a full-time basis, he will play a key part of our plans for the season ahead."
Newcastle get their Aviva Premiership campaign underway at home to Gloucester Rugby on October 16.