Hook into the WordPress Theme Customizer save action

I am facing the following issue :

I used to keep all the styling in a theme options page. When the user clicked the save button, i had a backend script that generated a css file with the changes so that they will not be output inline in each page. This has a lot of benefits, amongst them caching.

I have switched to the Theme Customizer, and everything is fine except i can't find a way to hook into the the "save" button. I would like to trigger a function that updates the content of the css file when that button is clicked in the backend.

Is this even possible ?

Thanks !