According to Contact Form 7 documentation
you have to set a JavaScript action hook. By using this hook, you can specify a JavaScript code that you wish to run after the form is successfully submitted. You will find the Additional Settings field at the bottom of the contact form management page. Simply insert the following line into it:
on_sent_ok: "your javascript code;"
If you want you can use following code to redirect to a new page with variables but it will send the variables to the $_GET
on_sent_ok: "location = 'http://yourdomain.com?myVar=somevalue';"
You can retrieve the variable as follows
$myVar = $_GET['myVar'];
Read more, also check add_query_arg.