His contract with the Pro14 side and the Welsh Rugby Union (WRU) ends in 2018.
The 28-year-old's move to France could hinder his international career as WRU's policy allows for the selection of only four players, that play for clubs outside Wales, to be included in the national team over the next two years.
Webb, who made his Wales debut in 2012, joins a long list of players that have recently left the region including Dan Biggar, Liam Williams, Taulupe Faletau, George North and Jamie Roberts.
(Reporting by Aditi Prakash in Bengaluru; editing by Sudipto Ganguly)
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