Academic postdoc: Interview process time insights
The time can be highly variable as there may be several people who need to give approvals and they may not all be available in a given time frame. There may be administrative issues that they need to resolve, etc. 

I suggest that you wait as long as it takes, but ask for an update after two or three weeks. But, if you have other options, don't give them up and continue any necessary process in case it doesn't happen after all. 

Keep a positive, but slightly skeptical attitude until you sign formally.