What you see is expected behavior.
Content scripts execute in a special environment called an isolated
  world. They have access to the DOM of the page they are injected into,
  but not to any JavaScript variables or functions created by the page.
  It looks to each content script as if there is no other JavaScript
  executing on the page it is running on. The same is true in reverse:
  JavaScript running on the page cannot call any functions or access any
  variables defined by content scripts.
http://developer.chrome.com/extensions/content_scripts.html#execution-environment
When you run console.info(myVar); from the page, the console of Chrome dev tools or from the injected script, it runs in the context of the page and thus sees the variable as defined.
However, when running the same code from inside of your extension code, you're operating in a completely different environment, so myVar is undefined.
You can work around this using shared DOM perhaps.
http://developer.chrome.com/extensions/content_scripts.html#host-page-communication
EDIT
Unless someone corrects me, the console.info(myVar); code below is injected into script element while still being executed in the context of the extension:
$("<script />", {
    html: "console.info(myVar);" // myVar points to extension's myVar, not page's
});
A simple test can be run by logging chrome.extension object or declaring myVar inside of the contentscript – the chrome.extension will be available and myVar will be logged exactly as defined in the contentscript.
The suggestion is to use an external script (which is also better for modularity), add it to web_accessible_resources and create a script element with a src property pointing to that external script.
The example extension code below alerts "test" when loading the test.html page with extension enabled.
manifest.json
{
    "name": "Test",
    "version": "0.1.0",
    "manifest_version": 2,
    "description": "Just a test.",
    "content_scripts": [{
        "matches": ["<all_urls>"],
        "js": ["contentscript.js"]
    }],
    "web_accessible_resources": [
        "myscript.js"
    ]
}
test.html (the visited page)
<!DOCTYPE html>
<html>
<head>
    <script>
        window.test = 'test';
    </script>
</head>
<body>
</body>
</html>
contentscript.js
var script = document.createElement('script');
script.type = 'text/javascript';
script.src = chrome.extension.getURL('myscript.js');
document.getElementsByTagName('head')[0].appendChild(script);
myscript.js (this is the external script that will run in the context of the page)
alert(window.test);