Lucic, who had to agree to be traded, said he spoke to former Boston Bruins teammate Jarome Iginla, who played 16 seasons for the Flames.
"I had a really good talk with Jarome," Lucic said. "He told me what a great hockey town Calgary is, how much the people are behind the Flames. It's a fan base that loves seeing effort. They obviously want to win, but regardless, they love the heart-and-soul guys, the guys who give their all, who don't compromise, which I like to think speaks to the way I play. …
"I like to think he knows me pretty well and that's why he took time out of his day to give me a call and help me with my decision. And he did help me make up my mind. I'm just grateful that I'm friends with one of the guys who I idolize most and that now I get to play for the team that he was most famous playing for."
This is the third trade involving players between the provincial rivals since Edmonton joined the NHL for the 1979-80 season.
On March 3, 2010, the Flames acquired defenseman Steve Staios for defenseman Aaron Johnson and a third-round pick in the 2011 NHL Draft.
On Nov. 8, 2013, the Oilers acquired goalie Laurent Broissoit and forward Roman Horak for goalie Olivier Roy and defenseman Ladislav Smid.
This offseason, goalie Mike Smith left Calgary to sign with Edmonton as a free agent, and goalie Cam Talbot, who played four seasons for the Oilers before being traded to the Philadelphia Flyers on Feb. 15, signed with the Flames.
"We haven't seen trades too often between us and Edmonton, so I'm sure guys on both sides are going to want to have big nights against their old teams," Calgary captain Mark Giordano told the Flames website. "It's going to add to the rivalry.
"It's always bittersweet when you see guys switching sides, leaving your team. [Neal] and [Smith] were good buddies, but Milan and Cam coming in, they're going to provide a spark. They're going to feel reenergized, looking for a fresh start."
A five-time 20-goal scorer, Lucic has 501 points (198 goals, 303 assists) in 890 games with the Oilers, Los Angeles Kings and Bruins. Selected in the second round (No. 50) of the 2006 NHL Draft, he won the Stanley Cup with Boston in 2011.
"Playing against him, you know he's a really fierce competitor," Giordano said. "He's a good leader, too, a guy who has won, who has been there and done it before. Everyone around the League knows how tough he is and that grittiness he can bring into your lineup.
"He's a guy that a lot of the players in the League, including myself, respect, and I think he's going to be a nice fit into our team. It will be nice to have him on our side of the ice now."
NHL.com staff writer Tim Campbell and correspondent Aaron Vickers contributed to this report