The last three chapters in the book of Daniel really form one unit. The traditional chapter divisions in part obscure this fact. Here we deal with Daniel chapters 10 and 11 together. (All bold are my emphases added. Square brackets [ ] indicate meanings of words. King James Version Easy-Reading Bible (KJVER) used.)
Daniel 10:1 In the third year of Cyrus king of Persia1 a thing [message] was revealed to Daniel, whose name was called Belteshazzar; and the thing was true, but the time appointed was long: and he understood the thing [message], and had understanding of the vision.
Daniel was mourning for three weeks when God somehow transported him in spirit and gives him his final vision. He finds himself besides the river Tigris, which was called Hiddekel (probably named that after the river in Eden of the same name).
Babylon though was located besides the great Euphrates river.
It appears that either an angel or God Himself in his theophany2 appeared to Daniel to reveal the vision.