The 30-year-old arrives as an injury dispensation signing following long-term injuries to Tom Croft (neck) and Craig Newby (knee) and will provide cover in the back row.
Phibbs arrives at Welford Road following injury to Ben Youngs (shoulder) and Academy scrum-half Scott Steele (ankle). The 30-year-old Australian has experience of Super Rugby with the Brumbies, where he worked with Tigers head coach Matt O'Connor.
He played for Exeter Chiefs last season, and featured against the Tigers Development XV in the Aviva Premiership Rugby A League semi-final at Sandy Park. He will provide cover for Sam Harrison and Micky Young.
Tigers Director of Rugby Richard Cockerill said: "Brett has done well for Gloucester during the past couple of years and he already knows the environment well at Leicester.
"We have had some injury issues in the back row with Craig Newby and Tom Croft out, and Jordan Crane coming back from long-term injury.
"Brett has played more than 100 first-class games and can come in and fit in where we need him to because he has plenty of experience."
Tigers will kick off their Heineken Cup season with a demanding trip to Toulouse on Sunday, 21 October following the announcement of the fixtures for the coming season.