We had the same problem with a shed....
We asked the LL to put in the lease specifically that the shed was for tennant use......then when we go to move in he has a bunch of stuff in it....mostly junk, kids toys, four lawn mowers, an old chair. Well, we really needed the space for our things, so we put all of his stuff outside in the yard and put our stuff safely in the shed, locked up. He came and got his stuff shortly after that. We didn't get huffy with him or anything, I think he is a very nice guy, we just told him our hands were tied, we have expensive things that needed locked up and we needed the space, the space we are paying for. His stuff was mostly decaying old kids toys and old lawn equipment no one had used in months.
Put his stuff outside in a safe spot, let him know, he'll come and get it. However, be careful, I pissed of a LL a short while ago because she refused to take care of her property and shortly afterwards we got the boot because our lease had ended. I would say try and be amicable, however, I just don't get LL's who want to rent properties and store their stuff there. I mean, these people are not giving you a free place to live, you are paying for it. My old LL had an old, nonworking dryer in her basement, an old, nonworking floor freezer and tons of other junk she refused to move. However, we could move it for her if we wanted it out.
I have to say, get it in writing before signing the lease. Most LLs words mean nothing, if it's not in writing, it didn't happen.