How should I ask my PhD advisor to let me work remotely...permanently?
Bring this up directly and immediately.

You mentioned in the comments that your advisor is out of town for a week but your wife must respond to the offer in a week. This doesn't leave you much choice, so email him immediately and ask to have an urgent phone call. 

Tell him openly about the situation and get his feedback. It is up to you whether to frame it as asking for permission or informing him of your decision.

However, you have to be prepared that he will not be willing to work with you remotely. You are putting your advisor in a potentially difficult position without much time to discuss it and basically giving him an ultimatum. I would have had an involved discussion about this before my spouse went on the job market (informing him that your spouse will be looking for a job and that you will be moving away if she gets an offer).