@ manifest.json:

{
    "manifest_version": 2,

    "name": "My extension",
    "description": "My extension does something",
    "version": "1.0",

    "permissions": [ "https://*.mysite.com/*" ],

    "background": {
        "scripts": [ "src/background.js" ]
    },

    "content_scripts": [
        {
            "matches": [ "https://*.mysite.com/*" ],
            "js": [ "src/content.js" ]
        }
    ],

    "browser_action": {
        "default_icon": "src/popup/icon.png",
        "default_popup": "src/popup/popup.html"
    }
}

@ src/content.js

var scriptToInject = '(function () { alert(window.globalVariable); })();';
var scriptElement = document.createElement('script');
scriptElement.textContent = scriptToInject;
(document.head || document.documentElement).appendChild(scriptElement);

// window.globalVariable always returns undefined.

// I've tried adding a long setTimeout() in scriptToInject to see if it's an issue of timing and the result is the same.

// When I check the browser console, globalVariable exists and has the expected value, but the injected script prints undefined.