The role of the UX department is to help software projects meet their goals by manipulating user behaviour. Therefore, the way to measure the department's success is to find metrics related to usability that directly reflect on the project's aims. This might seem a trivial observation, but it's vital that you measure success in terms your stakeholders care about.
So, if your company relies on e-commerce, you metrics could be % conversion, % repeat visits, amount-per-unit support required on orders, or any other relevant behavioural metrics. If your strategy requires social media exposure, your metrics will relate to the number of users who share links, the number of shae-ees (as it were) who convert, etc. etc. Deciding what your metrics are involves sitting down with the PM and teasing out the behaviours that are critical to success.
A word of warning: there are elements of your strategy that are difficult, no - impossible to quantify with simple analytics. Things like brand strength, trust, goodwill and pleasure cannot be measured by a server. Even surveys and qualitative research are pretty unreliable in this regard. That doesn't mean you should avoid these metrics, but it does mean you might need to communicate the limitations of measurement.
