Yes, if you are the custodial parent (the children are with you for more than half the year), then you are eligible to claim the EIC. When you go through the dependent section, you have to indicate that the other parent will claim them by giving them a signed 8332.
The one with whom the child spent the most nights is the custodial parent and can claim the child as a dependent. From what you posted that would be you. The IRS doesn’t care what your divorce arrangement is. The custodial parent can give the other parent a signed form 8332 to give the other parent the right to claim the dependency and child tax credit. The custodial parent retains the right to claim EIC and child care credit as well as file as head of household if otherwise qualified.
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