How should I ask my PhD advisor to let me work remotely...permanently? My wife plans to graduate in a few months. I have 1-2 years left before I defend and graduate. I'd like to move away with my wife so we can stay together. 

My work is entirely on a computer, so working remotely is entirely feasible. I have my own funding, so I do not need to stay in order to TA for pay. 

I typically meet once every 1-2 weeks with my primary advisor and "secondary advisor" (a research scientist who also mentors me and who frequently works more closely with me than my advisor). When I first began working with my primary advisor, I mentioned that I may need to work remotely for my final year. He said he didn't like the idea in general, but that he understands that life happens, and that we'd figure it out when the time came. 

The time has come, though I wouldn't move away for another two months. 

How should I breach the topic with my advisor(s)? 

This question is extremely relevant, but differs in that it asks this question for "extensive periods", whereas I'm asking about working remotely permanently. Several answers for that question involve staying away for progressively longer periods of time, but I'd prefer to not pay two rents.
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).