Argentina Under-20 international Iturbe will officially complete his switch to Eddie Howe's team subject to endorsement from the Football Association and a European work permit.
Bournemouth also have the option of making the move permanent at the end of the season for an undisclosed fee.
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Iturbe, who has scored three goals in 39 Serie A appearances for Roma, told Bournemouth's website: "It's a big opportunity for me to come and play in the Premier League.
"There were a few clubs that were interested but things happened pretty quickly and once this process was under way it was a straightforward decision for me to make.
"I didn't know a lot about Bournemouth as a club but the more I read and the more I found out how much they wanted me, it's an easy decision to go to a place where you feel really wanted."
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Iturbe was born in Argentina but grew up in Paraguay and began his career with Cerro Porteno before joining Porto aged 18.
Successful loan spells with River Plate and Verona convinced Roma to pay £17 million to sign him in 2014, but he didn't quite fulfil his potential in Italy.
Iturbe trained with his Bournemouth team-mates on Friday but will not be eligible for Saturday's trip to Leicester.
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