What should a contract Electrical Engineer deliver once a project is complete?
Design engineers won't like the idea, but as a design engineer my output for a project is a pile of paper. In a strict sense the working prototype isn't even required, though it will certainly put the client's mind at ease. :-)
We'll see that you need a lot of documents, and design engineers are not motivated to the task; read: they tend to make a poor job of it. They're better at other things. Therefore some companies have a documentalist in a team, to follow up the documentation phase.  

You need documents for every phase in the product's lifetime:  


  
  Production  
  Maintenance  
  Repair  
  Disposal  
  


Production
This is the most extensive, and will get the most focus (and unfortunately it often stops there).  


  
  Schematics  
  PCB layout (Gerber files, including drill)  
  Bill of materials  
  Datasheets for all of the BOM(!)  
  Mechanical drawings  
  Software sources (incl. project file)  
  Software object files  
  Test jig design and operation instructions (this can include all the above files!)  
  ICP (In-Circuit Programming) procedure  
  


Maintenance  


  
  Document(s) describing the procedure and tools for the product's maintenance, and how to replace consumables  
  


Repair  


  
  Document(s) describing how the product has to be taken apart for replacing defective parts. Specifics about how to replace parts which may fail during the product's lifetime (based on FMEA. You did an FMEA, didn't you?)  
  


Disposal  


  
  Document describing how the product has to be disposed of at it's end of life, with details about hazardous products and components.  
  


Whenever possible documents should have a version number and/or issue date (you don't always have control over this, especially with external documents, though most datasheets will at least have either a version number or publishing date).
You want all documents both in native format and in a standard electronic, printable format, like PDF. Specify how the electronic files have to be delivered: cloud (not a favorite of mine, confidentiality-wise), CD, DVD,...  

As a note I want to say that especially in small projects even project management isn't often interested in anything else than schematics and PCB layout. Every one of these projects, without exception, runs into trouble later on.