2 months seems too early. You hardly know him.
But you know your kids best. If they are likely to be hurt that you are seeing someone other than their dad, or feel threatened by a new man, then wait a while.
I would not tell them nothing. You will know after a year if he is for keeps. People come and go so be very careful bringing him onto your house whtn your kids are there. Also there is the green eye monster on everyone’s family so do not even go there and just wait 4 a while