How to turn a stray into a house cat?

Question
Hi Lisa,
how do I manage to turn a stray into a house cat?
Here's the background information:  This new cat of ours was
hanging out around the back yard of our house complex for
about 3 weeks before we took him in, last week.  He is clean (i.e.
he knows what a litter box is for...), affectionate, he doesn't
scratch anything in the apartment and he already has been
castrated either by an ex-owner or by the local pet-control
authorities.  I just don't know.
I took him to the vet last friday to get him checked out,
vaccinated and to find out if he has a chip (I live in Germany, and
in Berlin all free-walking cats and ALL dogs must be chiped).  He
had none. The vet thinks he must 9-12 months-old.  
Now everythings sounds great but there's a but... he wants to
spend the whole day outside and is quite vocal about it.  Since
I'm lucky to work from home, I let him go out after breakfast and
call him around lunch.  Around 3 p.m., I let go out for another
2-3 hours. After a week of having him, I already got him used to
a little mini  cow bell that I ring to indicate to him that it's now
time to come home, I wait 2-3 minutes and there he
is.  He gets a little cat candy for good behavior when he answers
the little bell.  He's already "half" of a house cat, I think.
Now my questions:  will I ever be able to turn him into a "only"
house cat?  I am doing this right with letting him go out and
enjoy the fresh air, the sun and doing whatever cats do?
Many thnaks for your answer.

Answer
It really just takes time. Letting him out less and less. Let him out later every day and call him back earlier. If you have cold winters, that is a good time to totally make him an indoor cat. He will appreciate the warmth of the house instead of the cold outside. Make alot of windows available to him, you might even go get one or two of those window beds that attach to the window sill for him to lay on. Cats that cant go out sure do enjoy laying in windows. and if you can, open at least one window, making sure there is a screen in it. then he can smell whats on the breeze and that may satisfy him.