The Turkish Super Lig champion has the option to sign the FIFA World Cup-winning midfielder for €16 million ($26.5 million) before 30 June next year.
It can also extend the loan by another season for €500,000 ($828,000), after which it will retain a purchase option of €13 million ($21.5 million) valid until 30 June, 2021.
"The club would like to wish Steven the best of luck for the future," a Roma statement read.
Nzonzi joined Roma from Sevilla last year, a month after his FIFA World Cup triumph with France in Russia.
He made 30 appearances in Serie A last season, scoring once, as the Giallorossi finished sixth.