TL;DR answer: Yes. As a gag/easter egg/cross-merchandizing/friendly jest/whatever, Spielberg and Lucas have placed enough canon information in their universes to infer that E.T. really is an alien from a species in a Star Wars Galaxy.
E.T.'s species were officially called The Children of the Green Planet, their planet was called Brodo Asogi
Background on the cross-over history:
The Children of the Green Planet are a cameo appearance of the famous aliens of Steven Spielberg's 1982 film E.T. the Extra-Terrestrial. These creatures were inserted in the movie to make good on a promise—after Steven Spielberg included a Yoda cameo and Star Wars toys in E.T., George Lucas promised to include an E.T. cameo in the next Star Wars film he made — The Phantom Menace.
Note: in this answer, any quotes are from Wikia article linked above, slightly reworded and improved.
Main Link #1: Visual evidence:
This is what ET looks like:
In "Star Wars Episode I: The Phantom Menace", in the Galactic Senate, we see the image of the senators from Brogo Asogi (not named in the movie) - who look 100% like E.T:
Main Link #2: Species/planet name:
"E.T.: The Book of the Green Planet" (a book from E.T. franchise which is the sequel to movie's novelization) mentions on page 19 that Brodo Asogi was one of many names given to E.T.'s homeworld, all of which translate to "Green Planet", and "Children of the Green Planet" to be the translated name of E.T.'s species.
In Star Wars Universe, the same homeworld name is given to the species in Cloak of Deception book (but the species name is not specified).
The species is named in HoloNet News Vol. 531 50 which mentions Senator Grebleips* of Brodo Asogi.
Other links:
First, the "easter egg - Star Wars in ET" that started the whole crossover:
When E.T. goes trick-or-treating with the children, he spots a child in a Yoda mask and begins to follow that child saying "Home… home…" (Composer John Williams included a snippet of his "Yoda Theme" from The Empire Strikes Back to accompany this scene.). This could be interpreted as E.T. recognizing a familiar species from his home galaxy.
Additional SW links to ET:
HoloNet News Vol. 531 50 also mentions that Senator Grebleips of Brodo Asogi funded an expedition to another galaxy. This is another reference to E.T., since E.T. visits Earth from another galaxy in the film.
Pat Welsh, the woman who did the voice for E.T. in E.T. the Extra-Terrestrial, also did the voice for the bounty hunter Boushh in Star Wars Episode VI: Return of the Jedi.
*Several people have made mention of the fact that Greblieps is Speilberg spelled backwards, as another related easter-egg.
