The short answer is that you have to be as dispassionate about the process as possible.
You're assuming they will be jealous. With mature adults, that's not really going to happen. What they will feel is disappointment, and you may even lose one or two in the following months as they see that there is no reasonable expectation of short-term advancement. It will fade, though, as they realize that they haven't lost anything, but rather didn't realize a gain they might have had.
However, you are correct to concern yourself with jealousy. Just remember, jealousy is an emotion, and any emotions you feed into the situation, even positive, only feed theirs. IF you are promoted, accept it quietly and graciously with a "Thank you" and a handshake when the manager announces it, and don't dwell on it.
In your first few days, be sure to be obvious about your respect of your team's abilities and contributions, both as a group and as individuals. Don't fawn over them, but a few "Good idea." and "Nice work." responses can go a long way.
There is one more thing in your favor, as well: Senior Developer is kind of a weird position: You have additional responsibility, but not really any additional authority. (Depending on your organization.) Most of the time it works against you, but in this case, it can work for you. You don't have to deal with the employee relations issues as a manager would. If you notice any problems with others' reactions to your promotion, it is not your issue to deal with it. Your manager still has that responsibility.
In fact, having a frank talk with your manager about where he wants you to "stop" managing and refer issues to him is very appropriate in the first couple of days after the promotion. If you're in a large organization, there may even be formal training/documentation. (In a previous company, all the HR policies for supervisors and managers were issued in a big purple binder. We called it, "The Barney Book.") Ask if something like that is available, and read it if it is.
Remember: Emotion feeds on emotion. Don't feed theirs, and any jealousy that crops up should calm down quickly.