After being knocked out by Los Angeles during the playoffs in the last two seasons, the Blues (39-13-6) made the move to better their depth.
The 33-year-old Miller won the Vezina Trophy in 2010 as the NHL's best goalie and is a two-time All-Star.
He boasts a career record of 284-186-56 along with a 2.60 goals-against average and a .916 save percentage.
The Blues also picked up veteran Ott who has 264 points (103 goals, 161 assists) in 673 career games.
The Sabres are the worst team in the NHL this season and fired general manager Darcy Regier in January. Friday's trade is the first move by new GM Tim Murray.
Halak, 28, has a 139-81-26 record with a 2.38 goals-against average and a .917 save percentage in eight NHL seasons.
The 26-year-old Stewart, a first-round draft pick in 2006, has 228 points (115 goals, 113 assists) in 377 career games.
Carrier was selected 57th overall in 2013 by the Blues.
(Reporting by Ben Everill in Los Angeles; Editing by Greg Stutchbury)