Rosetti, who was named best referee in Serie A four times in a row between 2006 and 2009 and officiated the Euro 2008 final between Spain and Germany, was hired by the RFU in 2011 in a bid to improve refereeing standards in Russia.
"We received a request from Roberto Rosetti to release him from his post due to family reasons," RFU's president Nikolai Tolstykh told reporters.
Rosetti, who retired after the 2010 World Cup finals in South Africa, expressed his special thanks to the Russian soccer authorities and all the referees in a statement, published on the RFU's web site www.rfs.ru.
"I chose Russia because I wanted to do something completely new, I was looking for a new challenge after officiating for 27 years in Italy," the 46-year-old said.
"My mission is accomplished and my family also needs me at this moment.
"The refereeing has improved during my stay. The Russian officials are on the right track and I'm sure they'll have a great future."