Yes. In the case of custodial vs noncustodial parents, the custodial parent wins.
You are the custodial parent. In order for the non-custodial parent to claim the dependent, you need to release the claim on Form 8332. A divorce decree does not override IRS ruling. See this LINK for more information.
If you both claim your child, you will get an IRS letter clarifying who has the right to claim. They will make the determination based on facts and proof of residency. Whoever loses, pays back the credit to the IRS.
Custodial parent and noncustodial parent. The custodial parent is the parent with whom the child lived for the greater number of nights during the year. The other parent is the noncustodial parent.
If the parents divorced or separated during the year and the child lived with both parents before the separation, the custodial parent is the one with whom the child lived for the greater number of nights during the rest of the year.