Does a Tower controller need to see an aircraft on final to give landing clearance? If there is an IFR aircraft on approach that has already received an approach clearance, and he reports being at the final approach fix but the controller does not have him in sight yet, can the controller give the aircraft clearance to land at this point, or does he have to wait until he has the aircraft in sight (which may be on short final)?

And what are the rules for (let's say) a VFR flight on final (maybe the controller can't see him due to rain over the field, etc.)?  Also, are there any reference documents (ICAO/FAA/Eurocontrol) that have information on this?

Here's a more specific IFR scenario: let's say the aircraft is making a CAT I ILS or maybe a VOR DME approach, in a non-radar environment. Does the tower need to see the aircraft before giving a landing clearance? The runway itself is clear from other vehicles or aircraft. Does the controller issue a "continue approach" instruction until he can see the aircraft and then clear it to land? O does he just issue the landing clearance at the final fix ( if the runway itself is clear)?
The FAA's ATC orders cover this for the US. Note that controllers can use radar instead of visual contact:


  3−10−7. LANDING CLEARANCE WITHOUT VISUAL OBSERVATION   
  
  When an arriving aircraft reports at a position where he/she should be seen
  but has not been visually observed, advise the aircraft as a part of
  the landing clearance that it is not in sight and restate the landing
  runway.
  
  PHRASEOLOGY−
  NOT IN SIGHT, RUNWAY (number) CLEARED TO LAND.
  NOTE−
  Aircraft observance on the CTRD satisfies the visually observed requirement.


(A CTRD is a Certified Tower Radar Display.)

As others have said, operations in poor weather would be very difficult if controllers needed to see all aircraft before clearing them to land.