Vina, 25, will join the Premier League side on a temporary basis until the end of the current campaign.
As part of the agreement, Bournemouth have the option to make the transfer permanent.
Vina joined Roma in the summer of 2021, going to make 44 appearances for the club in all competitions.
The Uruguay international was also a part of the side that won the UEFA Europa Conference League in May 2022.
The club would like to wish Matias the best of luck with this new adventure.
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