You can have your PHP code process the submission of your form and, at the end (once it is done processing the info), have it redirect the browser to your home page.
You can do that by using the
meta refresh tag in HTML. Example:
<meta http-equiv="refresh" content="0;url=http://www.yoursite.com">
Or the
header redirect function in PHP:
<?php
header( 'Location: http://www.yoursite.com/' );
?>
Whichever approach you choose, remember to do it at the end of your "processing"code, otherwise the page will be redirected before the form is processed.
REGARDS