The 25-year-old centre will link up with former Ireland lock Jeremy Davidson, who is the new head coach of the relegated Top 14 outfit.
Olding was acquitted of rape in March along with provincial and international team-mate Paddy Jackson, but their contracts were ripped up after other aspects of their behaviour that came to light during the trial were heavily criticised.
Both players were being lined up for a move to Sale earlier this month but the Sharks withdrew their interest. Jackson has yet to find a new club.
Brive announced the signing on their Twitter account, adding that they view Olding as a versatile threequarter who can also cover full-back.
While Olding, who has won four Ireland caps, and Jackson were found not guilty after a high-profile trial, major sponsors of Ulster Rugby voiced concern over their conduct.
Jackson and Olding had been accused of raping the same woman at a house party at Jackson’s home in June 2016.
The French club announced Olding’s arrival on their website yesterday afternoon.
A brief statement said that the Ireland centre “will continue his career in Brive for the next two seasons”.
The Brive statement also spoke of Olding’s “versatility” with the Ulsterman also having played at full-back and fly-half for the Irish province.
Earlier this month, English Premiership club Sale Sharks said there was “no substance” to reports linking them with both Olding and Jackson.
The BBC later learned that one of Sale’s main sponsors had raised concerns over the club being linked with the duo.
Two weeks after the players’ acquittals, the IRFU and Ulster revoked their contracts with immediate effect following controversy over details of social media and text messages which emerged during the trial.
An IRFU/Ulster Rugby statement said: “In arriving at this decision, the Irish Rugby Football Union and Ulster Rugby acknowledge our responsibility and commitment to the core values of the game: Respect, inclusivity and integrity.”
Ulster Rugby’s chief executive Shane Logan later said in an interview that he “could not envisage” Jackson or Olding playing for Ulster or Ireland again.
Olding emerged as one of the most talented young backs in Irish rugby after making his Ulster debut in 2011.
He made his Ireland debut in 2013 but injuries severely hindered his career and he made just three further appearances for his country before the rape charge led to him being stood down from playing duty in July 2017.