Centurion travelled to Europe to sign his contract with Anzhi, which has paid 7.5 million euros ($9.59 million) for the player.
"It is the first time that I have been to Europe. Everything was done very quickly but I agreed to go to Russia because I know it is the right decision for me and my family," the player said before boarding a flight bound for Russia.
"This transfer is a good thing for me and for Racing. I must spend six more months here but I am happy," he added.
Centurion, who turned 20 earlier this month, was one of the outstanding players during the domestic Torneo Inicial, in which Racing finished fifth, and also took part in this month's South American under-20 championship in Argentina.
Mega-rich Anzhi sits second in the Russian top flight, which is currently on its winter break.
Its squad contains the likes of Cameroon striker Samuel Eto'o and France midfielder Lassana Diarra.