What is the plan for her after detox? If she's going to rehab, or into treatment, I'd let her counselor/therapist in on it first, and either inform her, in person, while at a joint counseling session, or tell her on the phone while she is still at rehab. That way, they can help her process the news and help her plan for alternative living arrangements when she gets out.
And I agree with sauerkraut, you can be as positive as you can, assuring her that you really hope she takes this chance to heal and mend her relationship with the kids, and that for everyone's sake you plan to be as kind and fair to her as you can. But you also don't want to send mixed messages, so be sure you emphasize that there is too much water under the bridge for you to have any interest in reconciling.
My first husband has been sober for 14 years or so when I left him, and he still momentarily flipped out over the news and went into a bit of a depression (for which he got counseling, as well as leaning on his AA friends), and today we are still very good friends--I stay with him and his wife when I visit my (now adult) kids. When we finally did divorce (after an initial separation), we did it cooperatively and worked out all the details ourselves, splitting the cost of our respective lawyers (who just put into a document what we had agreed to).
My second husband had gone back to active drinking, and I had moved back across the country before I decided to file for divorce. He was thinking about moving to Africa (where his sister lived) and I didn't tell him in advance because I wanted to make SURE he was served before he could leave the country (he moved, but just to another state, a short time later).