The rapid development and spread of communication technologies is now becoming a global information revolution. Customers have a need for communication services, which could be flexibly configured in accordance with their Quality of Experience (QoE) requirements. Realizing the close connection between customer experience and profitability, the service provider has been placing more and more attention on customer experience and QoE. The traditional quality of service management method based on SLA (Service Level Agreement) is not sufficient as a means to provide QoE-related contracts between service providers and customers. The current SLA method is mostly limited and focused on technical aspects of QoS (Quality of Service). Furthermore, they do not follow on the network the principles and semantic approach to the QoS specification for a communication service using QoE parameters. In this paper, we propose a customer-oriented quality of service management method for future IBN (Intent-Based Networking). It is based on a new QoE metric on a scale from 1 to 5, which allows one to take into account the commercial value of e-services for customers. Based on this approach, the network configuration and functionality of network equipment automatically changes depending on customer requirements. To implement the new method of service quality management, an algorithm for routing data packets in the network was developed, taking into account the current load of the forecast path. The algorithm of billing system functioning in conditions of customer-oriented quality management in telecommunication networks has been created. To investigate the effectiveness of the proposed method of service quality management with the traditional SLA method, we developed a simulation network model with the implementation of two approaches. By conducting a simulation, it was determined that the proposed method gives an average gain of 2–5 times for the criterion of the number of customers who require high quality of experience of the service.