The 25-year-old, who played twice for Uruguay at the World Cup in Qatar last year, will join initially on loan with an option to buy, after the player failed to win a regular place in Jose Mourinho's Serie A side this season.
He is expected to arrive in the UK in the next 48 hours to finalise terms and undergo a medical with Gary O'Neil's Premier League strugglers.
Bournemouth dropped into the relegation zone following their 1-1 home draw with Nottingham Forest on Saturday and they have the worst defensive record in the league this season, with 42 goals conceded in 20 games.
Vina, who played 37 times for Roma last season, has struggled to match the playing time he enjoyed in his debut year in Italy after signing from Brazilian side Palmeiras, which included featuring as a substitute in the team's Europa Conference League final victory against Feyenoord.
He will become Bournemouth's second signing of the January transfer window after winger Dango Ouattara arrived from Lorient for £20million last week.