Does a Tower controller need to see an aircraft on final to give landing clearance?
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.