mime.types

...
image/webp webp;
...

nginx.conf

location ~ (.+)\.(png|jpe?g)$ {
	if ( $http_accept ~* webp ) {
		set $webp "A";
	}
	if ( $request_filename ~ (.+)\.(png|jpe?g)$ ) {
		set $file_without_ext $1;
	}
	if ( -f $file_without_ext.webp ) {
		set $webp "${webp}E";
	}
 
	if ( $webp = AE ) {
		add_header Vary Accept;
		rewrite (.+)\.(png|jpe?g)$ $1.webp break;
	}
}