The 22-year-old is set to replace Marcos Senesi, who left Bournemouth to join Tottenham Hotspur on a free transfer.
Silva has made 235 appearances for Benfica in all competitions and was named the Portuguese Primeira Liga's defender of the year when he helped the club to win the title in 2022-23.
He was also part of the Portugal squad that won the Nations League last year.
"Despite being only 22, he has already built an outstanding level of experience at one of Europe's biggest clubs," said Tiago Pinto, Bournemouth's president of football operations.
Bournemouth, who will play in Europe for the first time after earning a Europa League berth last season, kick off their Premier League campaign at Manchester City on August 23.
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