\ Although I also like what NYC laid out, from experience I might approach it in a less formal manner. Because 'poly' is so little understood it can actually become a block at first. I've found it's better to let people come to such 'labels' on their own.
I (we) have been in this exact position - and seen it a number of times in others.
What we found worked for us was to simply acknowledge the previous relationship, express the lack of understanding and how to cope/deal, and to explain that it's finally 'clear'. Nothing more.
Your explanation of now understanding how everyone's happiness is increased by it and that no 'harm' is coming from it is enough. You give your blessing and look forward to sharing in that happiness with both of them yourself.
It's simple enough..........
"I love you both - I'm happy if I can help make you both happy too !"