Getting your ex to agree to allow you to move out of state is a huge benefit for you. It is common for spouses to refuse to allow their ex-spouses to move away with the children, which can result in a legal battle.
However, in order to protect yourself, you should have that put in writing and file it with the court, which will either approve it or reject it. It would be extremely rare for a judge to reject a decision that both parents have mutually agreed upon. That would likely only happen if the judge felt that the decision was not in the best interests of the children. In some cases, a former spouse may agree verbally to allow the former spouse to move with the children, and for the spouse to later claim he or she did not consent, which is another reason to file the documentation with the court.
If your ex does not give his or her permission, you have a couple of options. The easiest is to get him agree to the move. You could consider agreeing to extra visitation with the kids over the summer and holidays in exchange for allowing the move. If he does not agree, you can go to court and ask for permission. You will need to show what’s in the best interests of the children, and how you can make sure your ex has enough contact with the children. If you move without the court or your ex’s permission, you are in violation of the court order.