sign off on
sign off on (something)
To give express formal approval of something. We're just waiting for the boss to sign off on the project before we start working. My thesis supervisor has to sign off on each chapter I write to make sure I'm staying focused on the topic.
sign off on something
to sign a paper, indicating that one has finished with something or agrees with the state of something. The publisher signed off on the book and sent it to be printed. I refuse to sign off on this project until it is done correctly.