I've only just seen this. I was adopted as a baby and have always know about it - I was so little that I have no recollection of being told, I just always knew. I think my adoptive parents handled it all very well.
I have 6 year old twin girls and they also know I am adopted, it hasn't been a big deal really. It probably started when they were about 4, when they said something along the lines of "Daddy came out of Nana J's tummy, and Mummy came out of Nana M's tummy", and I corrected them saying that Nana M couldn't have children of her own so she chose me because my mummy couldn't look after me. My DD's were very matter of fact and disinterested to be honest. They've brought it up now and then but it is all just "normal" to them and that's how I want it to be. I think keeping these things secret and then blurting it out when they are older or turning it into a big thing is not the way to go.
Slight problem with my adoptive brother as he has never mentioned the fact that he is adopted to his sons who are now 12 and 14. I keep warning him that my DD's may well bring the subject up and this has upset him. But I cannot keep it a secret from my children because of his views.
I'm in the process of tracing my adoptive mother but haven't had much success with my social worker. I'm thinking of trying to trace her by a different route but not sure how to. I have googled "adoption" and "tracing" but so many companies come up, some asking for lots of money. Not sure who is genuine or not.
I may start a new thread about this!!
Anyway, rambling on . In answer to the original poster, I would just be honest with your children, they do just take things in their stride and after all it is nothing to be ashamed of. It's rather special IMO, we were specially chosen.