There will be some immediate effects. Yes this does need to go through regulatory oversight, but Fox will start transitioning right away. This is what companies do when these deals get made, they have to be ready and running when the actual transition occurs, so they will decide on department restructuring, personnel and business unit alignment. They have to identify areas where there is redundancy, and unfortunately people will be identified for layoffs, severance agreements will be made, etc.
All of those things take time, so yes this is going to take a while to finalize, but it's not like these companies are going to sit around for the next 6-12 months twiddling their thumbs. Re-orgs will surely happen right away.