I developed a mozilla firefox addon and it passed the Full Review by AMO Reviewers and it is available in the store. Now I provide a new version of the same for update review. How long will this process take?
It can take anywhere between 10 minutes to 50 days, or longer.
How long it takes varies quite a bit based on the changes you have made, the current status of the queue and the reviewers who are currently active. For a fully reviewed add-on, the minimum time from submitting a new version to approval which I have experienced is about 10 minutes; the maximum was about 50 days. If the changes you have made require an admin reviewer, then it will probably be substantially longer.
Prior to the review being completed, the updated version will be visible on the version history page and can be installed from there (I have directed users to go there to install the new version when I have had a compatibility problem with a new release of Firefox). However, users of your add-on will not be automatically updated to the new version until after it passes review. If the new version of your fully reviewed add-on does not pass review, one option that the reviewer has is to provide the new version with preliminary review status. In that case, your users will not be automatically updated to the new version and the version which will be normally installed for new installations (without going to the version history page) will be the old fully reviewed version.