Single word request for "finished reading" or "completed reading"

You can either finish writing a book or reading a book, and it's almost always the latter.

In English, the sentence "I finished this book yesterday" is understood as reading, unless the context is specifically about authorship.

Building on @Valcor's answer, one could add completed to finished as a possible answer. Replacing finished by completed in Valcor's answer, one has:

In English, the sentence "I completed this book yesterday" is understood as reading, unless the context is specifically about authorship.

So you could replace finished reading or completed reading with either finished or completed with little chance of confusion:

I finished this book yesterday.

I completed this book yesterday.