Firstly, presuming you are Irish resident, this gift will be within the remit of Irish Capital Acquisitions Tax (CAT). He will have to get US advice on the US position.
If your son has not, since 5 December 1991, received any other gifts or inheritances from his parents, this gift will not create a tax liability as a person can receives gifts/inheritances from their parents of up to €520k before tax (at 20%) kicks in. If this gift brings him within 80% of that threshold he will be obliged to file a CAT return (form IT38).
If the property is situated in Ireland, he will be subject to Irish CGT at 20% on the uplift in value from the date of the gift and date of the sale, should he sell (or otherwise dispose of it).
You also need to bear in mind that you may have a CGT liability on the gift of the apartment to your son.