Morrison, 36, is a 15-year veteran who recently reached the 200-goal and 600-point plateaus for his career.
"I'm ecstatic," Morrison said in a conference call with reporters. "I'm thrilled. This is a tremendous opportunity to come to a team that I feel has as good a chance as anybody to compete for the Stanley Cup."
Morrison has four goals and seven assists in 28 games played this year. He spent time on injured reserve due to a left knee problem associated with his offseason surgery to repair a torn anterior cruciate ligament.
"I came back a tad early at the beginning of the year," Morrison said. "It felt fine and stable..I needed a little bit more time to work on some explosiveness. I know it's fine. There are no issues at all. Skating is getting back to where it's always been."
Morrison originally injured the knee in a game against the Hawks in early March of last year. Defenseman Niklas Hjalmarsson checked Morrison into the end boards and he was slow to get up. As he made his way to the Flames bench he and some Hawks on their bench had words but Morrison says that's all in the past.
"It's a dead issue," he said. "[I've] turned the page from that. There's no issues with that at all moving forward here. It's a done deal."
Hawks' general manager Stan Bowman said he's been talking to Calgary about Morrison for some time but the deal had to wait until the Flames got some injured bodies back in the lineup.
"It's been on our radar for a while," Bowman said. "There's a lot of attributes Brendan brings to the table which we've been looking for. He's a centerman. He's got a long pedigree of being an offensive performer. He still has a lot left to add to our group."
Bowman indicated the lack of experience for the Hawks at the center position was one reason for the deal.
"He's been a point producer in the past and I think he's also shown versatility recently to be able to play different roles on the team," Bowmans stated. "Plus he has a lot of leadership."
Bowman also said the trade had nothing to do with the hand injury to Jonathan Toews who missed the Hawks final game before the all-star break and is missing Sunday's all-star game. Bowman said Toews is "on target to play Tuesday" when the Hawks re-start their schedule in Vancouver against the Canucks.
Morrison played for Vancouver from 1999 to 2008 and is excited for a chance to play against the Canucks in his first game as a Blackhawk. He was asked if he was aware of the rivalry the two teams have with each other. They've competed in three consecutive postseason series.
"Very aware of it," Morrison said. "I don't think you could ask for a better first game really. It's going to be a playoff style game."
Bowman said he's not necessarily done looking for a forward. He's already on record saying he would like to add to his defense as well.
"We're still a month away from deadline so I'm not going to make any statements that we're done at anything," Bowman said.
Connelly, 25, has been with the Hawks organization since 2009 amassing 126 points in 211 games for Rockford of the AHL.
Jesse Rogers covers the Blackhawks for ESPNChicago.com.