The 33-year-old Tanguay returns to the team that drafted him 12th overall in 1998. He scored a career-high 29 goals for the Avalance in the 2005-06 season.
In 13 seasons with Colorado, Calgary, Montreal and Tampa Bay, the native of Ste-Justine, Que., has 249 goals and 513 assists in 922 games.
Sarich signed as a free agent with Calgary before the 2007-08 season. The Saskatoon native has 148 points (20 goals, 128 assists) and 1,051 penalty minutes in 915 games with Buffalo, Tampa Bay and Calgary.
Jones has spent the past six seasons with the Avalanche.
The native of Guelph, Ont., has accumulated 70 goals and 56 assists in 272 games.
O'Brien, a six-foot-three, 230-pound defenceman from Port Hope, Ont., has 88 points (13 goals, 75 assists) and 853 penalty minutes in 483 games with Anaheim, Tampa Bay, Vancouver, Nashville and Colorado.
"This trade adds needed size up front and grit on the back end while also allowing us to get younger," Flames general manager Jay Feaster said in a statement. "We like the fact that Jones plays a north-south game, drives hard to the net, kills penalties and is a right hand shot.
"O'Brien is a hard guy to play against, knows how to get under the skin of the opposition and stands up for his teammates. We are pleased to add both of these players to our organization."