Jones appeared in 22 games for the Lightning this season and posted a pair of goals with two assists. He has played 78 NHL games, all with Tampa Bay, which selected him in the fourth round of the 2005 NHL Entry Draft.
"Blair is a player that both [head coach] Brent Sutter and I are familiar with," said Flames general manager Jay Feaster. "He is a good-sized centerman and someone we feel will fit in well here with our organization."
Feaster was the Lightning general manager before joining Calgary. Jones also played for Sutter in junior hockey at Red Deer of the Western Hockey League.
Mikkelson had yet to play for the Flames this season after re-signing with the club in July. He was claimed off waivers from Anaheim on October 19, 2010 and appeared in 19 games for the Flames last season, but spent the first part of this season at the team's AHL affiliate in Abbotsford.
The 24-year-old Saskatchewan native has played 86 games in parts of three NHL seasons with Anaheim and Calgary. He has yet to score an NHL goal and has posted six assists.