Having said "Anochi Meis" why did Moshe need to add "E ineni Over es ha'Yarden"?
Rashi: Because even his bones were not destined to cross the Yarden (to be buried in Eretz Yisrael).
And why did he see fit to mention his death here?
Ramban #1 (on Pasuk 21) He was encouraging them to learn from him now, since he was destined to die there in the land of Mo'av, and would not be available to teach them when they entered Eretz Yisrael. 1
Ramban #2 (on Pasuk 21, according to Kabalah): It was a continuation of the warning (Pesukim 16-19) against making any images 2 - inasmuch as Hashem denied him entry into Eretz Yisrael for fear that they would worship him, a clear indication as to the seriousness of adopting an image as a a deity. 3
Seforno: He urgently needed to warn them, because he knew that, since he would not cross the Yarden with Yisrael, they would corrupt their ways. 4
Ramban: And that, after they arrived there, they should take care not to forget what he had taught them.
Ramban: And that is also what the Pasuk "Asher Tzivcha Hashem Elokecha" (Pasuk 23) is referring to.
See R. Chavel's footnotes.