Dancevic and Darcis will meet in the tie's first singles match on Friday, followed by Vancouver's Filip Peliwo facing David Goffin later that day.
Toronto's Daniel Nestor and Adil Shamasdin will play Ruben Bemelmans and Kimmer Coppejans in the doubles rubber on Saturday.
If necessary, Dancevic will take on Goffin on Sunday, followed by Peliwo meeting Darcis.
The tie will be contested on an outdoor clay court in Middelkerke, Belgium.
Milos Raonic of Thornhill, Ont., and Vancouver's Vasek Pospisil, the top-ranked male Canadian players, both had to sit out the event with injuries.
"We know we have a tall task in front of us but this is Davis Cup and I've always said rankings don't matter in Davis Cup," said Canadian captain Martin Laurendeau. "I've said that when we are favoured to win and I've said it when we are the underdogs. We came here to try and reach the semifinals and we have worked hard this week and prepared ourselves to give us the best possible chance of achieving that goal."
Canada is competing in the World Group quarter-finals for the second time in history after defeating Japan 3-2 in the first round in Vancouver in March. The team is looking to match the country's best ever result by reaching the semifinals, a feat first accomplished in 2013. Canada has a Davis Cup world ranking of No. 7 while Belgium is ranked No. 13.
Canada holds a 1-0 record against Belgium with the only meeting between the two countries being a 4-0 Canadian victory in 1913 — the first year Canada ever competed in Davis Cup.
The winner of this tie will move on to the World Group semifinals against the winner of a tie between Serbia and Argentina.