This happened to me with a BEA Viscount at Aberdeen in the 70s. I was on Tower, the BEA was transferred to me by APP at the ADN. I know that it was because the controller (Procedural) was sitting next to me. The pilot did not call me & I was intrigued to see when he would. There was no traffic to affect the a/c, so I didn't say anything & let it run.The pilot landed without a clearance to do so & made its first call to me clearing the r/w. I informed him of what had happened & he apologized. I reassured him that there was no real "incident" involved & safety had not been compromised. My concern was that he had learnt from the situation & would not let it happen again. I did not consider that anything was to be gained, in this case, from an official investigation.