The 23-year-old, who has two senior international caps for Portugal, has previously been linked with Manchester United, Bayern Munich and Manchester City.
However, the Spanish giants have all but won the race for Semedo's services in a deal reported to be in the region of £26m.
"FC Barcelona and Benfica have reached an agreement for the transfer of Nelson Semedo, pending medical tests on Friday in Barcelona," a statement on the Blaugrana website said.
"Semedo is an offensive full-back with superb physical attributes and he will be the ninth Portuguese to defend the Barca shirt."
Semedo played 63 times for Benfica in the past two seasons, winning two Primeira Liga titles.