Quite often during a home inspection I will note a gap between the concrete driveway and the garage slab on the inspection report. Taking the time to fill the gap will be worth the effort. Excess water under the slab will cause the slab to raise in the winter as the ground freezes. The gap can be closed using a filler/backer rod and a self leveling sealant filler material.
The first step is to clean the gap, blowing away all dust and debris. If there is any depth to the void you will need to fill it with a filler material, sometimes called backer rod, or backer rope. This is typically a closed cell synthetic material that looks like one of those float noodles that the kids use in the pool. But a size that is slightly wider than the opening you are trying to fill. Your local Rochester, or Southeastern MN building materials store will have these materials.
Next, force the backing materials into the opening using a putty knife until you have about ¾-1 inch below the concrete surface. The backer rod material will support the filler sealant and will expand and contract as the seasons change. It also provides a surface that will not stick to the filler sealant. If the filler sealant is attached to three surfaces, it may not expand and contract properly and pull away from the concrete.
After the backer rod is installed, add the self leveling concrete filler or urethane type caulk. This material will fill the void and is self leveling. This material is designed to adhere well to concrete and will expand and contract with the seasons. Always follow the manufacturers directions for installation and cure time. Proper installation will give you a great result that will keep the gap filled for years to come.