Light Yagami becomes a Shinigami

In the last episode though it says something like "that person will go to nothingness".

The first time I saw the series, that was my theory about what was going to happen to Light after he died. However, this has been denied several times.

There is an alternative ending of the manga in which Light appears in the Shinigami world after dying, and Ryuk appears before him. Light reveals rather arrogantly that he himself has always thought he would become a Shinigami after dying, to which Ryuk laughs at. Then Light suffers from a heart attack and goes back to life. Ryuk reveals to Light that his punishment is suffering from every death he had written in the Death Note.

After Light is hit by a truck (the second death he wrote), he starts laughing and tells Ryuk the number of deaths he had written (thousands!), telling him that his plan is to trick the Shinigami King himself to steal his Death Note (or something like that). Ryuk is rather surprised and then they go together. I think it's a great ending.

But no, he does not become a shinigami.