A combustor assembly for use with a turbine engine that includes a rotor assembly. The combustor assembly includes a casing that includes a plenum and a combustor liner that is spaced a distance from the plenum and that defines a combustion chamber therein. A transition nozzle extends between the combustor liner and the rotor assembly for channeling combustion gases from the combustion chamber to the rotor assembly. The transition nozzle includes a transition portion and a nozzle portion integrally formed with the transition portion. An annular flowsleeve is coupled radially outward from the transition nozzle such that an annular flow path is defined between the flowsleeve and the transition nozzle. The flowsleeve includes a plurality of openings extending through an outer surface of the flowsleeve for providing flow communication between the plenum and the annular flow path to facilitate impingement cooling of the flowsleeve.