Venezuelan Rondon, who became the club's highest scorer after arriving two seasons ago from Las Palmas, has signed a four-year contract, Rubin announced on their website.
The 22-year-old, who has 24 caps for his national side, was given leave not to join the club's pre-season tour to Italy last week because he was negotiating his exit.
Malaga also confirmed the move. They said on their website: "The player has a bright future ahead in the Russian league."
The Spanish club announced last week they were conducting an "internal restructuring" amid reports that owner Sheikh Abdullah Bin Nassar Al-Thani, of the Qatar royal family, wanted to sell the club after only two years.
Malaga midfielder Enzo Maresca claimed after their 2-0 friendly defeat by Juventus on Saturday that the club had also agreed to sell Spain playmaker Santi Cazorla, who has been linked with a possible move to Arsenal.
Maresca also warned that losing coach Manuel Pellegrini, whose wages are reported to be causing problems for the club, would be a "huge blow".
