As Devanur says, this will achieve your goal. It's worth reiterating that there is nothing inherently wrong with /index.php URLs as long as you cannot access the same content without /index.php. For instance, if www.site.com/page1/index.php exists as well as www.site.com/page1/, then this is duplicate content and should be fixed. I imagine this is your current situation because this is most common when /index.php is being added to URLs.
However, if only one version of every page loads and that version has the /index.php extension, this is not automatically bad. It's preferable for the extension not to be there for the sake of URL tidiness and because this does move the content one folder-level away from the root (not a huge issue, but probably best avoided) however.
If you go through 301 redirects to shift the old URLs to the new ones without /index.php, your rankings should not suffer. There might be a little bit of ranking fluctuation as Google indexes the new URLs and acknowledges the redirects, but nothing permanent. It's worth noting that this is not an absolute rule, however, and that there is always a risk of lowered rankings or rankings not returning to what they were before after a 301 redirect though.
Cheers,
Jane