Born in Carlisle, the 26-year-old tighthead came through the Newcastle Falcons Academy before playing two seasons at Nottingham.
Shields, who has represented England Counties, spent the next two seasons with Plymouth Albion and Darlington Mowden Park before securing a deal with Aviva Premiership side Harlequins last February.
The prop signed for English Championship side Rotherham ahead of the current season, but linked up with his new team-mates yesterday.
Shields said: “I’d like to thank everyone at Rotherham for their support and the opportunities that I’ve been given this season.
“However, I’m delighted to be joining Edinburgh at what is a very exciting time for the club, and I’m very much looking forward to working with Richard Cockerill and the rest of the players and coaches.”
Loosehead Rizzo had been brought in on loan by Richard Cockerill from his former club Leicester as cover for injuries and international call-ups. The initial six-week deal was extended but the Italian has now been recalled to Welford Road following the injury to England prop Ellis Genge.