The phrase "signed off on" simply means approval of a particular action or decision. Some synonyms for this phrase are "authorized," "endorsed," "validated," "commissioned," "sanctioned," "approved," and "ratified." All of these words convey the idea of someone in a position of authority giving the green light on a matter. For instance, when a manager authorizes a purchase, they are signing off on it. On the other hand, when a government official sanctions a policy, it means they have approved it. In summary, while the phrase "signed off on" is commonly used, it is essential to have an arsenal of different synonyms to use interchangeably depending on the context.