Good Evening,
@xmasbaby0's response is spot on, but I will add a slight caution. If this agreement had been put in place prior to 2009 the results would be different in that in a pre-2009 divorce decree, separation agreement, or the custodial spouse releases the exemption with a signed 8332 form - after 2009 the IRS only accepts a signed 8332 form that must be attached to the non-custodial parents tax return.
However, this does NOT mean that the custodial parent can ignore any decree or court order allowing the non-custodial parent to claim the exemption - they can be required to issue the 8332 form. They could be required by the court to do so or be in contempt, so this is something to keep in mind.
Full rules regarding who can claim can be found in IRS Pub 501. Hope this helps.
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