<p>We have a large ASP (classic ASP) application and we would like to convert it to .NET in order to work on further releases. It makes no sense continuing to use ASP as it is obsolete, and we don't want to rewrite it from scratch (Joel Spolsky tells you <a href="http://www.joelonsoftware.com/articles/fog0000000069.html" rel="noreferrer">why</a>).</p>

<p>Is there a way to convert it from ASP to ASP.NET automatically?</p>

Microsoft has an article up on MSDN that talks about
Migrating ASP Pages to ASP.NET
. They basically tell you to install .net on your computer/server and the transform one page at a time. ASP and ASP.NET can co-exist so can can rename each page to "aspx" as you go. You should note, however, that session state and application state are not shared between ASP and ASP.NET pages (See
@mdb's answer
for a workaround on that problem.)
There is also
The ASP to ASP.NET Migration Assistant
, but I'm not sure that project/program is still active. You can try it by downloading from this page:
http://www.asp.net/downloads/archived/migration-assistants/asp-to-aspnet/