It marks an end to a long and sometimes painful saga for both firms.
LVMH backed away from the deal in the midst of last year's global lockdowns, saying its original bid for Tiffany looked too high.
After a bitter legal dispute, the pair eventually agreed on a lower price, cut by 425 million dollars.
Now the French luxury goods group is wasting no time shaking up management.
On Thursday (January 7) it named new bosses for Tiffany.
Senior Louis Vuitton executive Anthony Ledru becomes chief executive.
And Alexandre Arnault becomes an executive vice president.
He's the son of LVMH boss Bernard Arnault, and formerly ran Rimowa, the group's luxury suitcase brand.
Analysts bet LVMH will now try to expand Tiffany product ranges to target younger shoppers.
It's also expected to make a big push in Asian markets.
The conglomerate has already signalled changes on the design front, saying Tiffany's artistic and brand chiefs will both be leaving.
LVMH shares were up around 2% by mid-afternoon Thursday.
