The Venezuela striker, 22, skipped Malaga's pre-season trip to Italy to complete a move that is believed to have cost in the region of 10 million euros.
"He has signed a four-year contract with Rubin," the Russian club said on its website.
Rondon, who has also played for Las Palmas, had been linked with Italian giants Juventus and Premier League side Tottenham.
Malaga announced on Thursday they were undergoing a process of "internal restructuring" amid reports owner Sheikh Abdullah Bin Nassar Al-Thani, a member of the Qatar royal family, wanted to sell up after only two years.
As well as Rondon, the "restructuring" is expected to lead to the sale of other leading players, including midfielder Santi Cazorla to Arsenal, and possibly the departure of Chilean coach Manuel Pellegrini.
Cazorla is also absent from the tour to Italy.
Spanish media reported the 27-year-old, who made his debut for Malaga in August 2011 after joining from Villarreal, was in London this week to tie up the Arsenal switch.
Malaga confirmed on Friday they had sold midfielder Apono to La Liga rivals Real Zaragoza, where he was on loan for the second half of last season.
But the exit of Rondon hints that they are willing to offload all their star players in a bit to reduce debts that most thought would be managed by the wealthy owners who bankrolled the initial spending spree.