The 31-year-old Phibbs made five appearances for Tigers, including in the win over the Maori All Blacks,
He moves to Irish to provide injury cover for Ireland International Tomás O'Leary.
London Irish director of rugby Brian Smith said: "With Tomás sidelined for what could be the remainder of the season, we've been pro-active in signing Pat Phibbs.
"I have great respect for his ability, he's an experienced scrum-half, good organiser and strong defender. He also has knowledge of the English season so he's a pretty good fit for us."