A system for wrapping loads comprising a rotary platform rotating around a vertical axis, a wrapping head having a reel of film for covering a load, the wrapping head being configured to be selectively associated with a moving machine having a rotatable connection and a plate with removable connections, a support frame configured to support the wrapping head when not associated with the moving machine, the support frame being placed outside of the moving machine and configured on linear rails, the wrapping head including attachments for removable connection to the support frame, the removable connections of the moving machine being configured to support and connect the wrapping head when the wrapping head is associated to the moving machine, the rotatable connection of the moving machine being configured to rotate a plate having the removable connections and to move the wrapping head connected to and supported by the plate toward or away from the support frame so as to facilitate replacement of the wrapping head.