The moves were announced Monday night.
Kottaras, acquired from Kansas City last week, is due $1,075,000. Murphy will earn $825,000.
Besides Samardzija and Wood, the Cubs offered contracts to five other arbitration-eligible players: pitchers Pedro Strop and James Russell, infielders Darwin Barney and Luis Valbuena, and outfielder Nate Schierholtz.
Chicago's roster now stands at 37 players.
If arbitration-eligible players are non-tendered by their clubs, they become free agents. Bard might still return to the Cubs.
Bard, who was claimed from the Boston Red Sox in September, has battled inconsistency and injuries since a two-year run (2010-11) in which he gave up just 91 hits in 147 2/3 innings as one of the game's top setup men.
The Red Sox gave up on Bard late this past season following his struggles with a move to the rotation. Bard, 28, appeared in just two games for the Red Sox in 2013 and was plagued by injuries. He never appeared in a game for the Cubs.
Information from The Associated Press was used in this report.