"Real" success needs to tie to the realization of business value which might only be evaluated months or years afterward.
The project success factors should be agreed upon at the beginning of the project and documented in the project charter between the Sponsor and the PM. It should be the Sponsor (ideally) identifying the project as a success or not. Of course, he/she can take into account quality, stakeholders' satisfaction, etc.
When the project achieves all deliverables and products within planned time, cost, and budget and at the expected quality. Assuming that the stakeholders' needs are reflected in plans.