Donnelly and Beattie join Bayonne
Bayonne will also sign Scottish flank Johnnie Beattie from Castres.
Donnelly, who has signed a one-year contract, had spent the last two years with Montpellier but was not part of the matchday 23 for Sunday's Top 14 play-off victory over Castres.
Likewise, Beattie, who spent two years with Montpellier before the last two with Castres, was not involved. He has signed a three-year deal.
Donnelly, 34, was capped 15 times by the All Blacks and played for Highlanders, Crusaders and Blues in Super Rugby.
Beattie, 30, has played 38 times for Scotland and began his career with Glasgow.
Bayonne, who secured promotion back up to the Top 14 this season at the first time of asking, have already signed a raft of players for next season in a bid to strengthen their squad in a bid to maintain their top flight status.