The 31-year-old tighthead, who has 28 caps, joins from Edinburgh where he made 130 appearances and scored six tries.
"It is great to have a player of Geoff's talent and experience joining our squad next season," said London Irish director of rugby Brian Smith.
"He is a genuine international tighthead who has performed exceptionally well in the recent Six Nations. We will have plenty of competition in the front row next season that will only benefit the squad."
Cross, a qualified doctor, added: "Moving down to London Irish is a fantastic opportunity for me. Having met with Brian, discussed the vision of the club and seen the new training facility it was clear to see the intent the club has moving forward. Leaving Edinburgh was a difficult decision and I will leave with many fond memories, however I am excited to be moving to Sunbury and look forward to the challenge ahead."