From Chambers Dictionary 11th Ed.:
ORIGIN: OFr Ebreu and L Hebraeus, from Gr Hebraios, from Aramaic ʻebrai (Heb ʻibrī), literally, one from the other side (of the Euphrates)
From Oxford English Dictionary 2nd. Ed.:
ME. Ebreu, a. OF. Ebreu, Ebrieu (nom. Ebreus, 12th c. in Hatz.-Darm.), ad. med.L. Ebrę̄us for cl.L. Hebræus, a. Gr. Ἑβραῖος, f. Aramaic ﻋebrai, corresp. to Heb. ﻋibrī ‘a Hebrew’, lit. ‘one from the other side (of the river)’;
late O.E., from O.Fr. Ebreu, from L. Hebraeus, from Gk. Hebraios, from Aramaic 'ebhrai, corresponding to Heb. 'ibhri "an Israelite," lit. "one from the other side," in reference to the River Euphrates, or perhaps simply signifying "immigrant;" from 'ebher "region on the other or opposite side." The noun is c.1200, "the Hebrew language;" late 14c. of persons, originally "a biblical Jew, Israelite."
From Collins English Dictionary:
[from Old French Ebreu, from Latin Hebraeus, from Greek Hebraios, from Aramaic `ibhray, from Hebrew `ibhrī one from beyond (the river)]