The person ultimately responsible for defining the product holds the role of product manager / product strategist, whatever their explicit title might be in the company.
For example, in an early stage startup, one or more of the co-founders is typically the product visionary. He or she drives the primary market research process to learn about the customer and end user, and iterates on a proposed solution to solve their problems until they find something that works for their customers. In that case, the founders are doing the product definition themselves.
In more established teams, when the engineeering organization gets to a certain size, it is time to add a full time product manager to the team, whose job is to be the CEO of the product (so the CEO can be the CEO of the company). The product manager would define the product in that case.
The product manager's product definition will be influenced by input from the user experience designer and/or user experience researcher(s).