I'm also not a lawyer, but including both license files and adding to your README that your project is dual-licensed under both licenses at the user's choice should be sufficient. GitHub should also detect both licenses and show them in the project's side bar.
If you copy-pasted the licenses, just make sure to adapt the MIT license, as it includes the year and name of the copyright holder. You should adapt these to your project.
You can take a look at the MIT license website which has the placeholders.
Fun fact: On GitHub, if you add a file in the web UI and include "LICENSE" in the file name, it gives you a button to choose a license template. Then you can see common license options and a summary of what they do. It also allows you to fill in details like the year and copyright holder.