DisturbedNeo has the correct date; Celeborn and Galadriel assumed political control of Lothlórien around T.A. 1980 or 1981. The date comes to us from Unfinished Tales, which contains a detailed history of the pair from the Second Age onwards. There are two competing drafts describing the event:
It was not until far on in the Third Age, when Amroth was lost and Lórinand was in peril, that Galadriel returned there, in the year 1981.
Unfinished Tales Part 2: "The Second Age" Chapter IV: "The History of Galadriel and Celeborn"
[I]t was not until the disaster in Moria [T.A. 1980], when by means beyond the foresight of Galadriel Sauron's power actually crossed the Anduin and Lórien was in great peril, its king lost, its people fleeing and likely to leave it deserted to likely occupied by Orcs, that Galadriel and Celeborn took up their permanent abode in Lórien, and its government.
Unfinished Tales Part 2: "The Second Age" Chapter IV: "The History of Galadriel and Celeborn" Amroth and Nimrodel
The first draft is dated by Christopher Tolkien to approximately the writing of The Lord of the Rings, but he's no more specific than that; it could be any time from 1937 to 1949. The second draft is dated to 1969, and most probably represents Tolkien's final (recorded) thoughts on the matter in his lifetime.
However
I feel it important to point out that Galadriel was never Queen of Lórien; this is something Tolkien felt the need to call out specifically, so I find it worth being clear on (emphasis mine):
After the disaster in Moria [in the year 1980] and the sorrows of Lórien, which was now left without a ruler (for Amroth was drowned in the sea in the Bay of Belfalas and left no heir), Celeborn and Galadriel returned to Lórien, and were welcomed by the people. There they dwelt while the Third Age lasted, but they took no title of King or Queen; for they said that they were only guardians of this small but fair realm, the last eastward outpost of the Elves.
Unfinished Tales Part 2: "The Second Age" Chapter IV: "The History of Galadriel and Celeborn" Amroth and Nimrodel