CBC will broadcast the game — only the third regular-season game ever to be played outdoors in Canada — which will be the first NHL contest played in a retractable-roof stadium.
"With one of the world's great facilities as the setting, and one of the world's most scenic cities as the backdrop, the 2014 Tim Hortons NHL Heritage Classic at BC Place in Vancouver will honour hockey's Canadian heritage," NHL commissioner Gary Bettman said in a release.
"With the excitement, the entertainment, the competitiveness and the fun of this game, the Canucks and Senators will create special memories for hockey fans everywhere."
BC Place, which has a capacity of 59,841, is home to the CFL's B.C. Lions and the Vancouver Whitecaps of the MLS.
"The NHL Heritage Classic allows our sport to further celebrate the history of the game while doing so in a unique venue," Canucks president and GM Mike Gillis said. "We look forward to showcasing our city, province, team and fans this upcoming March."
The 2014 edition of the Heritage Classic follows the 2003 game in Edmonton between the Oilers and the Montreal Canadiens, and the 2011 contest in Calgary between the Flames and Habs.
Ottawa and Vancouver have some history, albeit through their predecessors, as the two cities went head-to-head in a best-of-five series for the Stanley Cup in 1915. The Vancouver Millionaires of the Pacific Coast Hockey Association swept the Senators, then of the National Hockey Association, to claim the Cup.