Rajeshwar Singh, 29, and Gagandeep Kaur, 30, shared an apartment in Milan with the victim, 29-year-old Mahfab Ahadsavoji, whose body was found off the island of Lido last week and identified through finger-prints.
The couple allegedly strangled Ahadsavoji to death after she refused a sexual advance, ANSA reported.
The duo then stuffed her body into a luggage bag with rollers and took it by train to the northern city of Lecco with the intention of tossing it into Lake Como, police said.
A Venice taxi driver told police the duo paid him 500 euros for the return trip to Milan.
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Ahadsavoji, a known costume designer in Iran, was in Milan for a two-month course at the renowned Academy of Fine Arts of Brera.
A postmortem revealed that Savoji died of asphyxiation.