Kanye West and Jay-Z's friendly greeting at Diddy's 50th is no surprise to people close to them -- turns out they've squashed their legal feud, and have already gotten back to making money ... together.

You'll recall ...both members of the "Watch the Throne" duo lawyered up in 2017 when Ye split from Tidal, Jay's streaming service. Kanye said he was owed $3.5 mil, and their professional relationship was on ice.

Cut to Saturday night at Diddy's crib ... where they smiled, shook hands and seemed totally cool with each other ... because they are. Sources connected to both moguls tell us they quietly reached an agreement in the Tidal dispute earlier this year. We're told both men are satisfied with the outcome and they're moving forward.

Case in point ... when Kanye put on his first opera, "Nebuchadnezzar," last month at the Hollywood Bowl ... it streamed exclusively on Tidal. We're told there will be future collabs for Ye and Tidal, too.

Of course, they've had an up and down relationship -- putting it mildly -- for years ... even before the Tidal lawsuit. Kanye was famously upset that Beyonce and Jay-Z didn't attend his wedding to Kim Kardashian -- and went off on him during a 20-minute rant onstage in 2016.

Seven months later, Jay dropped his "4:44" album, and the track, "Kill Jay-Z" featured lyrics clearly firing back at Ye for that rant.

Although people were surprised to see their "reunion" at Diddy's party ... our sources say Jay and Kanye have crossed paths from time to time in the last year, and have been totally cordial with each other. Diddy's event was just the most public meeting.

We're told they've put the legal wranglings behind them, and money's no longer an issue between them -- after all, they've both got mountains of it. While their biz beef is buried, and they've repaired their fractured personal relationship ... don't expect "Watch the Throne 2" anytime soon.

Ye's promised he's only doing the Lord's music from here on, so ... IF it does ever happen, guess we'd just be watching a different throne.