Iginla last played in the NHL for the Kings in 2016-17 and had his No. 12 retired by the Flames last season.
"I'm excited, as a Calgary Flames fan and as a friend of his," Iginla told the website. "I had the chance to play with him, we were linemates and we've kept in touch. For whatever reasons, it didn't work out in Edmonton. I don't know why. But as a fit in Calgary? A great guy, good teammate, and they don't have a player like him.
"... Last year watching the Flames, it looked like they had a lot of fun playing together, they truly enjoyed each other's company, were happy for each other. He can thrive in that atmosphere. He'll add to that culture. I think the fans in Calgary are going to enjoy him too."
Lucic has four seasons remaining on the seven-year contract he signed with the Oilers on July 1, 2016, after playing one season with the Los Angeles Kings. He played his first eight NHL seasons for the Bruins and won the Stanley Cup in 2011.
"You're always aware of where he is when you're out there against him," Calgary captain Mark Giordano told the website. "To be honest, he's gotten me a couple times in my career with some big hits.
"He's a presence out there. He's a guy, that when you play against him, you know where he's at all times. And he's a guy that can get to the front of the net and make things happen too. He plays the game hard and he plays it the right way."
Lucic scored 39 goals in 243 games with Edmonton, falling from 23 his first season to 10 then six.
"Initially, I thought no way -- but no way -- am I going to the other side of the Battle of Alberta," Lucic said. "But after talking to (Flames general manager) Brad [Treliving], talking to (coach) Bill [Peters], talking to (assistant) Geoff Ward, who I spent seven years with in Boston, and some guys who'd played in Calgary, it seemed to sound like a place I wanted to go, where the fit was right."