Sources with direct knowledge tell TMZ the former foes have actually been cordial behind the scenes for months. Obviously, Sunday night's performance was the first public display they'd worked things out ... but our sources say the reconciliation happened some time ago.

Of course, the next question fans want answered is what does the renewed friendship mean for Migos and the chances Quavo and Offset release new music together?

Our sources say as of now, there's not a plan in place to record anything as a duo -- the goal of the BET show was strictly to honor Takeoff, not a marketing ploy. In fact, it's still not even known if the two would ever use the Migos name again in releasing potential future projects.

What's more ... our sources say if Migos ever was revived, Quavo and Offset would never replace Takeoff with someone else.

TMZ broke the story, things were still nasty between Quavo and Offset during the Grammys in February when they got into it backstage ... but thankfully, that's now a thing of the past.

As we reported, the BET crowd erupted as Takeoff's verse from "Hotel Lobby" pumped through the speakers inside DTLA's Microsoft Theater before Quavo and Offset took over to perform the trio's signature breakout single, "Bad and Boujee."