Word for officially and legally confirm a decision

Maybe try ratification.

Ratification is defined in the Oxford Dictionary as:

the action of signing or giving formal consent to a treaty, contract, or agreement, making it officially valid

E.g.:

"ratification of the treaty raised problems in several member states"

It's RULING.

According to Merriam-Webster's Dictionary :

ruling

: an official or authoritative decision, decree, statement, or interpretation (as by a judge on a point of law).

Here's an example from Reverso.context.net:

"The author further notes that the Court of Appeal mentions in its ruling that its rulings are final, and does not indicate any other remedy available to the parties."