In a statement on their official website, the Chinese Super League (CSL) club announced "Contra and his coaching staff will soon arrive in Guangzhou" to complete the deal.
Michel, who has been on loan at Getafe from Valencia, will follow his Romanian coach to China for his first stint outside Spain.
The 26-year-old attacking midfielder, who has scored one goal in 12 La Liga matches for Getafe, has also played for Levante in his career.
Contra, who represented Romania 73 times between 1996 and 2010, has been in charge of Getafe since March but, according to reports in the Spanish media, the 39-year-old claimed the La Liga outfit had asked him to leave to help them financially.
Guangzhou R&F have been looking for a new coach since Sven-Goran Eriksson quit in November, after leading the club to a third-place finish in the CSL in 2014.