Bricks, Masonry, Asphalt and Concrete - Concrete joint filler help

I recently bought a 7 year old house and just outside of the garage door, where the floor slab meets the concrete driveway (at the apron), there is a gap that is approximately 3/4 to 1 inch wide by approximately 2 inches deep. This joint is exposed to the elements and the remnants of a prior (e.g.) asphalt type seal is visible in places. Also the rebar tying the garage slab with the driveway is exposed.

I went to Home Deposit and the only concrete joint filler/sealers they had were for a 1/4 inch maximum width. An employee told me I needed rope caulk for concrete and to check with a local concrete supplier. Does this sound right? I have Googled for a fix 'til I'm blue in the face. I need to fill that gap with a water tight seal that will last a long time and don't think wood (red or cedar) is going to do it. It get's pretty hot here so a liquid or semi-liquid asphalt product will get messy. Any suggestions are greatly appreciated. ...Peace

Do not fill the joint with a solid, hard material.

Get "backer rod" at the big box (flexible foam rod - different sizes) and put it in the joint, depressed below the surface. This will allow you to force a flexible caulk into the joint and stick to the sides.

Get a good caulk or you will be spending more time and money in the future.

Dick