There is no physical reason why gravitational potential energy is negative.
The key of potential energy (any potential energy, not just gravitational) is where you define it to be equal to 0 and you are allowed to define this point to be anywhere. However once that point is defined, then all the maths must follow the same convention.
And just to make things confusing, for GPE the zero point is often defined differently depending on the situation you are dealing with.
When you are thinking about potential energy of say your textbook in your room, then it would make sense to say that the book has 0 potential energy when it is on the ground, because if you let go of it on the ground it will not move and so no change in energy (potential to kinetic) has occurred. If however you pick it up then it has gained some potential energy because now it can be dropped and it will fall (so converting potential energy into kinetic energy). This obviously is using a simplified version of gravity and potential energy as it does not take into account how the force on an object due to gravity decreases the further it is from the source.
If, however, you are dealing with a situation like a planet and a satellite, then you must use the more general form of gravity and a more general form of potential energy. The satellite will experience 0 force when it is placed at an infinite distance from the planet and so this is the logical place to set the zero point of the potential energy. It is logical, because only when the satellite is an infinite distance away from the planet has it truly escaped the gravitational influence of the planet and it will not move if you let it go.
So now that the zero point has been set, the behaviour of the potential energy does not change. The satellite will have less potential energy the closer it is to the planet (just like the textbook having less when it is on the ground as opposed to being in the air) and so for this to fit with the zero point then the GPE must be negative.
I hope this helps, it has been a while since I did HSC physics so I don't know how it is explained in the textbooks. The main point is really that as the GPE decreases as it gets closer to an object and as it is convention that the GPE equal zero when it is an infinite distance away then it means that the GPE must be negative.
