The Hurricanes must expose one goalie in the NHL Expansion Draft, with the list due June 17. Carolina also has Cam Ward and Eddie Lack, each under contract through next season.
The Vegas Golden Knights, who begin play next season, have to select at least 20 players under contract for next season among their 30 choices (one from each NHL team) in the expansion draft.
Darling had an NHL salary-cap charge of $587,500 this season, according to Cap Friendly.
Carolina traded a third-round pick in the 2017 NHL Draft, which they acquired from the Ottawa Senators, to acquire Darling. The Hurricanes had 11 picks in the draft.
"This is a bit of a gamble, but one we believed was worth taking," Francis told the newspaper. "This is why we accumulated these picks, and we still have 10 left. It was worth the risk."
Darling, 28, was 18-5-5 with a 2.38 goals-against average and .924 save percentage in 32 games (27 starts) this season as the backup to Corey Crawford. He's 39-17-9 with a 2.37 GAA, .923 save percentage and four shutouts in 75 NHL games (64 starts), all with Chicago.
Darling played in five Stanley Cup Playoff games in 2015, helping the Blackhawks win the Stanley Cup.
"Obviously he's a big guy (6-foot-6, 232 pounds) and he's extremely competitive, which you can tell if you watch him play," Francis said. "He was more than serviceable in his role in Chicago. He has been hoping to get the opportunity to be a No. 1 goalie and his numbers indicate he's capable of being a No. 1 goalie ... [He was] genuinely excited about the opportunity and the fact we stepped up and showed interest in trading for him."
Ward and Lack were the primary goalies this season, when Carolina tied for 26th in the NHL with a .901 save percentage.
Ward, 33, started 61 games and went 26-22-12 with a 2.69 goals-against average, .905 save percentage and two shutouts. He has spent his entire 12-year NHL career with the Hurricanes and signed a two-year contract prior to this season.
Lack, 29, played 20 games (18 starts) and went 8-7-3 with a 2.64 goals-against average, .902 save percentage and one shutout. He was acquired in a trade with the Vancouver Canucks at the 2015 NHL Draft.