Since there has been no answers here, I will answer my own question.
What I ended up doing was to install a clean TFS 2010 server, then creating the Team Projects that I will need.
I then downloaded the TFS Integration Platform from Codeplex. It promises to be able to migrate the code. Using the TFS Migration Shell I got a user friendly dialog allowing me to configure the migration source control folders.
It is currently running the migration, which I suspect will take a long time. I will update here with the results when it has finished.
Update
The migrationran over a weekend and failed twice, and I did not really have the time to figure out why. Apparently it found some inconsistencies in branches in our old source control branch. I am sure you can use the TFS Integration platform to do this, but, depending on your current situation, there might be some work to get it done. (They also state that it is a Beta-release).
I ended up importing the entire old TFS using the supported upgrade path (TfsConfig.exe /import). This gave me a very clean upgrade with almost everything working, but including the old stuff that I was trying to leave behind. I guess I will have to go through and delete that manually, and change the process templates to our liking, and so on.
2nd update - 2010-08-09
The TFS Integration Platform has been updated some times since I tried my luck with it, so you might have better results than I had, if you use the current release. If you do try it, or make experiments with it, please post an answer here.