An engine output control apparatus is used on a vehicle having an engine driven by a drive-by-wire system and includes a device for setting a first target engine control amount in accordance with an amount of operation of a manually operated engine control member; a device for detecting wheel slippage and for setting a second target engine control amount at which wheel slippage is reduced when wheel slippage exceeds a predetermined value; a device for setting a third target engine control amount at which constant-speed running of the vehicle is maintained when a manually operated constant-speed control member is actuated; and a selecting device for selecting one of the first, second, and third target engine control amounts. The selection made by the selecting device is based upon a determination of whether wheel slippage has exceeded a predetermined value and whether the manually operated constant-speed control member has been actuated. A setting device is provided for setting the engine output control amount based upon the target engine control amount selected by the selecting device.