Here is the official report of foreign student exchange (2004 in English).
http://www.mext.go.jp/a_menu/koutou/...020201/001.pdf
And there are many college or univercity who accept foreign students.
For example, Tokushima national university accepts
1) students nominated by Embassy,
2) students nominated by Univercity and
3) students recruited in Japan.
These are described in a Japanese page
http://www.tokushima-u.ac.jp/article/0011136.html .
However, I can not find corresponding page in English.
There must be good description n English. I will look for them.