The letter is postmarked Berlin and dates December 10, 1915.
"The boldest dreams have now been fulfilled," Einstein wrote in the letter, rejoicing in his theory's success.
Einstein had set out the key elements of the general theory of relativity in four magisterial papers submitted to the Prussian Academy of Sciences between November 4 and 25, according to the British auction house Christie's.
Einstein's general theory of relativity is one of the most important developments of 20th century physics.
The postcard, written in German, opens with news of an intended journey to Switzerland, after Einstein was assured that his eldest son, Hans Albert, wished to spend time with him.
Einstein signed off the letter with 'greetings from your happy but rather worn out Albert.'
The postcard is a part of a collection of letters written by Einstein to his college friend Besso currently up for online auction at Christie's. The bidding for the items in this collection closes on December 6.