Sources with direct knowledge tell TMZ ...Kelly was filming the singing competition Wednesday when she got an email saying the hotly-contested prenup was upheld in full by the judge. We're told the prenup segregates all assets and income derived during her marriage to Brandon Blackstock.

Kelly accumulated the lion's share of assets, including the Montana ranch where Brandon is currently living. He was contesting the prenup and wanted their properties split, along with income she earned during their marriage, but the judge shut him down.

We're told the celebration on the set of "The Voice" got personal. Our sources say Blake Shelton had recently terminated his relationship with Blackstock, who managed him for years.

The other judges who were there, including Ariana Grande, participated in the celebration.

Clarkson's lawyer, Laura Wasser, had argued during the trial on the prenup, that there had to be accountability when someone signs a contract -- in this case, a prenup. The judge clearly agreed.

The divorce has been "bifurcated" -- meaning the actual declaration that the marriage is over has been separated from the property settlement and custody issues. The actual dissolution of the marriage should be finalized within days. Kelly has been awarded primary custody on a temporary basis, because Brandon moved to Montana. It seems by validating the prenup, most issues have now been resolved.

As for the ranch, because the prenup was validated, Kelly -- who purchased it -- now has the right to sell it.