Smith, 29, played 28 games for the Maple Leafs last season, collecting nine points (four goals, five assists) with four penalty minutes.
The six-foot-one, 195-pound forward also had 10 goals, 16 assists and 10 penalty minutes while serving as captain of the American Hockey League's Toronto Marlies in 2013-14.
Smith made his Maple Leafs debut October 8 against Colorado, becoming the 900th player in franchise history. The native of Ottawa missed 24 NHL games due to a broken hand.
The Maple Leafs selected the 19-year-old Valiev in the third round, 68th overall of the 2014 draft.
The 6-1, 205-pound native of Nizhnekamsk, Russia, posted five goals and 23 assists with 68 penalty minutes and a plus-27 rating in 55 games with the Kootenay Ice of the Western Hockey League last season.