I would try to address this a different way than some of the others who have given advise. Yes, while they are old enough to 'get over it', they, and you, will still have to deal with a blended family for at least another 4-5 years, so it does involve everyone in the family for quite some more time.
You don't mention much about your fiancee. Does he get along with your children? Were he and the kids fine before the engagement? How did they take you 'dating' this man? These are all questions that need answers before anyone can pass judgment or give accurate advise. Anyone stating the kids should just "get over it" without knowing how the kids feel about this man, is just stupid advise.
If you're kids and your fiancee have always had issues, this may be the time to find out why. Do they think he is taking the place of their father? Are they concerned in the way he treats you? Does he have children they don't get along with? Is this a fairly new relationship going really fast? Has he been involved with the children much? Have you been dating for a long time?
These are all valid points which need to be addressed.
If you haven't been dating this man long, give them time and maybe slow down the process a little bit. Start off by staying at each others house, then living together, then the full force moving in and then finally the wedding. Just because you fell head over heals for the man in a short amount of time doesn't mean your kids have to.
On the other hand, if they have no had issues until the announcement of the engagement, or if you have been with the man for a long time and you believe they should have adjusted by now, it may be a plain case of fear of change. Yes, it has been only the three of you for so long, but if the children, no matter how old they are, are scared of change, then it is your responsibility as the parent to help this through this. NOT just say 'oh well, this is how it's going to be' and leave it at that.
Don't get me wrong, yes, you deserve to be happy, but you also need to take into consideration what is best for the children. As some state, in reality they are going to be out of the house in 4-5 years...why would you want to make this the worse years they are going to remember.
I will state I am a little bias on this subject. When I was younger, my mother married a man whom me and my brother did not get along with. Although she didn't want to be alone, and he made my mom 'happy' as she put it, he just couldn't get along with us kids. Mind you I was 13 and my brother was 8 when they started dating. Like you, she too raised us by herself for many years before he came around.
He was never abusive to any of us, but we never saw eye to eye on many things and life was terrible. After 3 years, and at the age of 16, I had finally had enough, and I guess so had he. He had my mom choose. Both of us could not live in the same house without causing havoc.
She didn't say straight out she chose him over me, but rather stated "He makes me happy and I'm not going to tell him to leave. You'll be gone soon enough anyways and should start being an adult". That night he once again started fighting with me and I left. Mind you my mom didn't stop me, he made her happy and she wasn't going to tell him to leave. Remember, I was only 16 years old.
I lost my mom because 'she wanted to be happy'. She could not see all the things he was doing like me and my brother could. She loved him, and that was all she cared about.
It has been 13 years now, she was still with him, and my brother went through a touch time last year and needed family support. My brother went to her for help, and once again, just like he did with me, my mothers husband gave her a choice, either my brother or him. Gladly, my mother chose my brother this time, and her divorce was finalized a couple months ago.
Please don't choose your man over your kids. Don't break that bond you have created over the last 8 years doing it by yourself.
Sit with the kids and find out why they feel this way! They may know or feel things you don't see being lovestruck with this man. He might be the best man in the world for you, and if so, I'm all happy for you. But please ... Don't stick it to your kids without knowing why they feel this way!