The other day I was discussing with my friend whether Light Yagami himself became a Shinigami after death. Well I disagree with that.

The very first day Ryuk came into the human world to meet new owner of the Death Note, he warned Light that whoever uses it can neither go to hell nor heaven. Also they say that there's a mistranslation of this line in  Japanese, which actually translates to "The question of heaven or hell is invalid.". Either ways it creates the same idea that Light couldn't be reborn as a Shinigami.

In the last episode, they also reveal that all humans will eventually end up in "MU" or Nothingness no matter their deeds on Earth. But since people like to believe in their own fan-made theories I guess it's okay.