On Tuesday, the pop star's marriage to Dalton came to an end in the books -- with their previously agreed-to settlement taking effect ... and making them unattached legally, ending their nearly three-year marriage, according to legal docs obtained by TMZ.

There wasn't much they needed to do other than wait for this one -- it'd already been signed, sealed and delivered for a while ... the wheels of bureaucracy just had to take effect.

As we reported ... Ariana filed to dissolve their marriage in September 2023 after the former couple separated eight months earlier. About a month later, she and Dalton had settled up -- one of the fastest celebrity divorces on record. The pair had a prenup and no kids.

We broke the story -- per their agreement of their settlement, Ariana had to cough up a single lump sum payment of $1,250,000 to Dalton and split the sale of their L.A. home. She will also throw Dalton $25,000 for his lawyers’ fees.

You may recall ... Ariana hooked up with Dalton during COVID in 2020 – and, at first, everything was going swimmingly. But, once the COVID restrictions were lifted, their relationship quickly went downhill as Dalton, an L.A. realtor, was taken aback by Ariana's celebrity and other lifestyle changes. Plus, she got busy again as an A-list star.