General manager Scott Howson announced the move on Saturday. Rivet, 36, is expected to join the club in time for Sunday's game at Nashville.
Rivet has 49 goals and 187 assists with 1,148 penalty minutes in 909 career games with the Montreal Canadiens, San Jose Sharks and Sabres. He has four goals and 19 assists in 69 career Stanley Cup playoff games. He has spent the past three seasons in Buffalo, serving as the club's captain. This year he has one goal, two assists and 12 penalty minutes in 23 games.
The Blue Jackets, in the middle of the playoff race in the Western Conference, were looking for an experienced defenseman.