This starts with your business case. In that document you should have documented all of the benefits that you expect to accrue and that justify the money to be spent on the project. Integrated with your business case is a benefits realization plan, which documents the benefit to be accrued, who is accountable for accruing it, the metric(s) used to measure this accrual, the frequency of measurement, and what the targets are that define success. If a benefit cannot be measured it should not be in your business case.
What you need to make this a success is buy-in and accountability from your management. For example, if a benefit is reduced effort and therefore headcount the person who owns the staffing budget for that unit has to be accountable for achieving that reduction. Beyond that, you also need clear ownership of the process of assessing benefits, specifically someone in your organization who is not in a conflict of interest in terms of benefits realization.