The Tunisia international, 23, arrived at the Ligue 1 club on Wednesday after undergoing a medical.
Khazri leaves Bastia following a five-year spell at Stade Armand Cesari.
"The sports project makes me feel immediately envious. This club has ambitions and play at the top of the table. It's good for me," he told Bordeaux's official website.
Khazri scored six goals in 32 appearances during the 2013-14 campaign.