The deal will play the 26-year-old $550,000 at the NHL level and $105,000 at the AHL level.
Mueller scored 32 goals in 2011-12 for the Milwaukee Admirals, also tying for the AHL lead with three overtime goals. His eight game-winning goals ranked second in the league. Mueller became the first Admiral in five years to score 30 goals in a season, and also participated in his first AHL All-Star Classic.
Mueller also appeared in four games with Nashville last season, and in 19 career NHL games with the Predators has recorded three assists.