The success of the product owner depends on how much invested the person in this role feels and he/she understands the true meaning of being a product owner. But to measure the success, we can define some parameters LIKE:

• Strength of Product Backlog – If the product backlog stays healthy with prioritized items and has good user stories to worked UPON by the teams.
• Constant delivery of Value – Whatever the teams are delivering by the end of the SPRINTS, should be ADDING value to the clients.
• Attaining of Release Goals – At the start of a release, whatever the items teams commit should reach the end line. The goals should be met.
• Understanding of Product Vision by team members – The delivery team is able to understand and comprehend the vision from the product owner, they should be able to understand why are they creating the product, what value is it going to add to the customers.
• Defining a successful Product Roadmap is again important for the realization of the release goals.
• Lastly, the customer is satisfied.

There can be many parameters to access the success of this role, every organization has its own SET of KPIs for it. But most importantly it should the collaboration between the product owner and the teams plus the product owner and the customer.