Gulum was born in Melbourne and played for Australia at under-23 level before opting to represent Turkey, the country of his parents, in senior ranks.
The 30-year-old central defender has seven caps for Turkey and joins Adelaide from a stint on loan in China from his Turkish club Besiktas.
New Adelaide coach Marco Kurz says Gulum is "just the beginning of what we are aiming to do".
"I am sure we will have more good news in the coming days," Kurz said in a statement on Monday.
Gulum's dual citizenship means he won't be classed as a foreigner, paving the way for United to sign more overseas players.
"I'm joining Adelaide with the ambition of being successful and I have every intention of making sure that happens," Gulum said in a statement.
"Australian football has given me so much and I'm here to give back to it by working very hard."