The pair obelisks were carried to Iseum, the Temple of Isis in the ancient Rome and erected there. But it is unknown what happened after that, since the people lost the interest in the obelisk.
In 14th century, this obelisk stood at the east of Santa Maria in Aracoeli on the Capitoline hill (Monte Capitolino). And this has been standing there for about 100 years, but seemed to have toppled and moved out somewhere. Then, Duke called Ciriaco Mattei obtained this obelisk from the Senators of Rome as a present in late 16th century (in 1582? 1584?), and erected it in his Villa at Celimontana. But the Villa was devastated and the obelisk seemed to have toppled again in the 18th century.
Then, the Spanish statesman Manuel de Godoy (1767-1851) temporarily stayed in this Villa, and restored the ruin. The obelisk was re-erected in 1820 (Other source says 1817) by him at the place where stands here at present.