The 31-year-old is due to win his 82nd Scottish cap against Fiji in Lautoka on Saturday. That will rank him third alongside Gregor Townsend among Scotland's most capped players, while his move to France will bring to an end a 10-year link with Edinburgh.
Brive reached the semi-finals of the Amlin Challelnge Cup last season, but ended up in the relegation zone in the Top 14 and will be playing in ProD2 as a result in the 2012/13 camapign.
Despite his switch overseas, Blair remains fully committed to extending his Scotland career.
"I've never made a secret of my desire to play in France at some stage during my career and I'm delighted that it will be with Brive," said Blair.
"It's a lovely place with an incredible support and I'm really looking forward to meeting up with them after the Scotland tour.
"There were a number of considerations that I wanted to take into account for me and my family and Brive ticks a lot of the boxes that matter to us."