The second-row, 29, will leave Edinburgh after spending three years in the Scottish capital.
"Sean Cox is a very experienced player with well over 100 first class matches under his belt," Irish director of rugby Brian Smith told the club's official website.
"He's an outstanding lineout forward with a high work rate and offers plenty around the park. He's bought into what we want to achieve and will add real steel in the pack."
Cox has represented England at Under-18, Under-19 and Under-21 levels.