"I am very happy to join Basel, it's a step forward in my career," Ivanov, who signed a three-year contract, told local media. The deal includes an option for one more year.
The 25-year-old centre back, capped 35 times by the Balkan country, joined Partizan from Russia's Alania Vladikavkaz in 2011 and also had a successful spell at CSKA Sofia. He won two Serbian league title with the Belgrade-based side.
Basel blew a three-goal lead but hung on to beat Maccabi Tel Aviv 4-3 on aggregate on Tuesday to seal a place in the Champions League playoffs.
Ivanov will not be eligible to play for Basel in the playoffs having already played for Partizan in the Champions League's qualifying rounds.