The Sharks also signed defensemen Artemi Kniazev and Nikolai Knyzhov; and forward Zachary Gallant to entry-level deals Tuesday.
General manager Doug Wilson called the 29-year-old Prout a ''responsible'' defender who will provide a good net-front presence for the Sharks. Prout had one goal and one assist in 20 games last season for Calgary and has played 262 career games with Columbus, New Jersey and the Flames.
The 26-year-old Brodzinski played 13 games last season for the Los Angeles Kings, recording two goals and one assist. He has six goals and five assists in 54 career NHL games.
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