A club statement said the 22-year-old would remain on the English south coast for the rest of the season with the Cherries retaining an option to make the switch permanent for an undisclosed fee.
Iturbe, known for his explosive pace, was born in Argentina but has played for Paraguay at full international level. However, his last cap was for the Argentina Under-20 side.
He joined Roma in 2014 and scored three goals in 39 Serie A appearances.
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Iturbe has already trained with his new team mates but is not eligible for Saturday's Premier League game at high-flying Leicester City.
Bournemouth, whose stadium only holds 11,000, have made a good fist of their first ever season in the English top flight and are 16th at the halfway point of the 38-game campaign -- three points above the drop zone.
(Writing by Mark Meadows; Editing by Tony Jimenez)
