our lovely nanny of 5 years left, when my ds was 3.5. I thought he'd be traumatised - actually he was fine. She was married and we told him that she wasn't going to be coming every day any more because she was going to spend more time with her husband, because her husband loved her and missed seeing her. But that X was going to be looking after him instead, and lovely nanny would come and visit when she could (we parted on excellent terms and see her every couple of months).
Children at the end of the day don't really care about nannies leaving - it is surprising but they don't - they may be a little sad etc but I've never known one to be traumatised by it, as long as mummy and daddy are still there (and assuming they do have a relationship with mummy and daddy, as clearly you do with your son).
Tell him the truth - she won't be coming every day any more because she is spending more time with her husband/grandparents/paretns... that granny will be coming to look after you which is LOVELY aren't you LUCKY! Make it a positive thing. If he asks when he will see her again, tell him that she is busy for a little while but we'll try and organise something soon. After a while he'll forget that something was meant to be organised.