Corporate pilot reported after being cleared for takeoff they began to enter the runway then stopped when they observed a Cessna on short final.

Narrative

Asked for an intersection departure with ZZZ Ground Control ([Runway] XXL at Taxiway 1); was given updated instructions by Ground to hold short of XXL at Taxiway 1. When approaching and holding short of XXL and Taxiway 1; I switched to ZZZ Tower. I told Tower that I was holding short of XXL at 1 and that I was ready for departure. They cleared me for takeoff. I read back my takeoff clearance and began to taxi onto the runway. As I was running my final takeoff checks; I began to look to the right to check the runway is clear and at about 2 o clock; I see a high wing Cessna ahead and above me on the runway. I begin to apply brakes and simultaneously hear the Cessna mention that there is an aircraft on the runway he is landing on. I keep holding my position in the active area of the runway. I have not completed my turn to line up yet. I kept holding my position and looked for clarification that I was cleared for takeoff on XXL. I held my position until tower had me line up at wait on XXL and Taxiway 1. I read it back and lined up and wait. I visually saw the Cessna clear the runway and then was given my takeoff clearance again by the Tower. I read back the takeoff clearance and departed the airport with no further issues. When I got on with ZZZ [TRACON] I requested the ZZZ Tower phone number so that I could call them later to get a better understanding of what had happened. When I landed at my destination; I voluntarily called the Tower to discuss what had happened and they mentioned that they were currently reviewing the playback and would call me later. They called me later to say that I was in fact cleared for takeoff and that it was a controller error.