John Gill Commentary Jeremiah 51:63

"And it shall be, when thou hast made an end of reading this book, that thou shalt bind a stone to it, and cast it into the midst of the Euphrates:" — Jeremiah 51:63 (ASV)

And it shall be, when you have made an end of reading this
book
To the captive Jews; and having also said the above words by way of prayer and approbation:[that] you shall bind a stone to it, and cast it into the midst of
Euphrates ;
a river by which Babylon was situated. The book, being read, was to be rolled up again, and then a stone tied to it, and cast into the middle of the river, where the waters were deepest, and from where it could not be taken up; and this was a sign confirming the above prophecy; compare with this what was done by a mighty angel concerning mystical Babylon, in which there is an allusion to this, (Revelation 18:21) .