To use some old fashioned words... you were dating. You decided to "go steady" with the boyfriend. Now you both are deciding that you don't want to "go steady" but want to continue to date each other and date other people. Maybe and even up to becoming another person's lover. You now have a new "understanding."
Where is problem?
Was your plan to just go and jump this new guy's bones tomorrow?
Or was the plan to go out on a few dates to see what he is really like before deciding anything more?
I mean, he has a voice of his own here too. Maybe he's not interested in dating you or being your lover. Maybe he's not cool with poly situations. Maybe he's cool with it but you get to know him and find out he plays the accordion on weekends and the constant noise totally turns you off. (I try to joke to keep it light.)
Don't jump the gun "what iffing" all kinds of things in your head. BREATHE. If you want to ask him out on a date, ask him out. Find out what you need to find out. THEN see what you see.
At this point -- you have run it by your BF and he's informed and on board. So... don't overthink it. If this is what you want to do, do. *shrug* Decided this is NOT what you want to do after all? Do not do. Don't go all tempest in a teapot over it working yourself up. Whatever you pick is totally ok and totally right for YOU. You are being honest, nothing is hidden here.
You get to choose how to write your life story. YOU are in charge of your behavior and choices. Isn't that a neat thing?