Knowledge base adoption
The adoption or usage rate of your knowledge base should be the primary metric by which the success of your strategy is judged. If the percentage of those who are using the KB out of the total number with access to it is high, your knowledge base is likely widely trusted, usable, and comprehensive.
Note: It's important to look at the adoption rate regularly. Many knowledge bases are trusted and comprehensive when they're first set up, but go stale over time, leading to a downward trend in adoption. This is a good catalyst for a knowledge audit, and to institute a governance structure.
In general, an adoption rate of ≥80% indicates a successful knowledge base.
Average age of submitted knowledge
Knowledge should be refreshed as necessary with any knowledge base (internal or external). A stale knowledge base (for instance, one where the average age of submitted knowledge is ≥1 year) is less likely to be trusted -- and so less likely to be used. While some information may only need to be updated on a yearly basis (ex: benefits documentation; slide deck templates), others may need to be updated on a monthly or quarterly basis (ex: quota outlines; competitive intelligence; team structures).
Note: If possible, set your knowledge to "expire" on a specific interval which will cause it to fall into a untrusted state, and force the owner to look at it and reverify its accuracy as necessary.
Any knowledge that hasn't been reverified in over a year must be looked at and either updated or removed from your knowledge base in order to maintain its usability.
General usability of submitted knowledge
Knowledge that's difficult to find or understand won't be used. Try and keep your knowledge as short and to the point as necessary, and if possible, break it down into specific, individual pieces. For example, rather than adding 5 30-page documents, break each section of that document down and make it its own entry in your knowledge base, and link off to related pieces where it makes sense:
This way, each of those pieces is individually findable, but they are also usable as a whole. This ensures that a specific piece of knowledge is quickly available (and easily updatable) without requiring extra time to sort through, as longer documents require more reading and searching.