An electromagnetic connecting device comprising: a rotary member rotatable around an axis; an armature arranged in an axial direction parallel to the axis with respect to the rotary member; a leaf spring (22, 51, 61) including a base end portion fixed to the rotary member, and a free end portion connected to the armature; an electromagnetic coil; an attracting member (2, 11) arranged on an opposite side of the rotary member across the armature, accommodating the electromagnetic coil, and configured to attract the armature by moving the armature in the axial direction against a spring force of the leaf spring (22, 51, 61) when an electric current is supplied to the electromagnetic coil; and an anti-vibration member formed by an elastic material, wherein the leaf spring (22, 51, 61) includes: a moving portion that includes the free end portion and moves in the axial direction together with movement of the armature; and a non-moving portion that includes the base end portion and does not move in the axial direction, characterized in that the anti-vibration member is fixed to the moving portion of the leaf spring (22, 51, 61), and the anti-vibration member includes: a stopper that comes in contact with one of the rotary member and the non-moving portion of the leaf spring (22,51,61) from a side of the armature; and a damper that comes in contact with the armature from a side of the rotary member. a rotary member rotatable around an axis; an armature arranged in an axial direction parallel to the axis with respect to the rotary member; a leaf spring (22, 51, 61) including a base end portion fixed to the rotary member, and a free end portion connected to the armature; an electromagnetic coil; an attracting member (2, 11) arranged on an opposite side of the rotary member across the armature, accommodating the electromagnetic coil, and configured to attract the armature by moving the armature in the axial direction against a spring force of the leaf spring (22, 51, 61) when an electric current is supplied to the electromagnetic coil; and an anti-vibration member formed by an elastic material, wherein the leaf spring (22, 51, 61) includes: a moving portion that includes the free end portion and moves in the axial direction together with movement of the armature; and a non-moving portion that includes the base end portion and does not move in the axial direction, characterized in that the anti-vibration member is fixed to the moving portion of the leaf spring (22, 51, 61), and the anti-vibration member includes: a stopper that comes in contact with one of the rotary member and the non-moving portion of the leaf spring (22,51,61) from a side of the armature; and a damper that comes in contact with the armature from a side of the rotary member. a moving portion that includes the free end portion and moves in the axial direction together with movement of the armature; and a non-moving portion that includes the base end portion and does not move in the axial direction, characterized in that the anti-vibration member is fixed to the moving portion of the leaf spring (22, 51, 61), and the anti-vibration member includes: a stopper that comes in contact with one of the rotary member and the non-moving portion of the leaf spring (22,51,61) from a side of the armature; and a damper that comes in contact with the armature from a side of the rotary member. a stopper that comes in contact with one of the rotary member and the non-moving portion of the leaf spring (22,51,61) from a side of the armature; and a damper that comes in contact with the armature from a side of the rotary member.