CDC has confirmed that it will issue a comprehensive order later today. Effective 1/26. That's a bit longer than it should be, but it's better than not happening. According to CDC statement, either a negative test or adequate medical proof of recovery are required prior to boarding and air carriers are directed to deny boarding to anyone who cannot produce one or both.
Same as already exists for UK-US travel and easily fits within existing law.
Air carriers really pushed hard for this and it's just taken a while.