I’d recommend spending a little bit of time and wrap your project in DrWatson.jl which was made exactly for this purpose. In the documentation you also find a very nice overview how such a project can be initialised with ease.
But in general, yes, a Project.toml will describe the environment and the dependencies and a Manifest.toml will even set each of them to a very specific version, so your environment will be fully reproducible.
Here is a quick tutorial in the DrWatson docs, it’s really easy to set it up: DrWatson Workflow Tutorial · DrWatson