The 22-year-old becomes Jose Mourinho's first signing of the summer transfer window, with Sky Sports reporting that United will pay a fee of £30.7m ($39.1m) to Benfica for his services.
The Red Devils are yet to agree personal terms with Lindelof, while the move is also subject to international clearance and a medical.
United came close to signing Lindelof in the January transfer window, but ultimately decided against making a move for the Sweden international as key defenders returned from injury.
"Manchester United is pleased to announce that it has reached agreement with Benfica for the transfer of Victor Lindelof, subject to a medical examination, international clearance and personal terms," a statement released by the club said.
"A further announcement will be made once the transfer is complete."
Lindelof made 32 league appearances in Benfica's title-winning 2016/17 season, scoring one goal. He played the full 90 minutes of Sweden's 2-1 World Cup qualifying win over France in Stockholm on 9 June.
The Daily Mail says Lindelof will fly to Manchester for a medical on 14 June – a day after Sweden play a friendly against Norway in Oslo.
The 22-year-old has won three Portuguese league titles with Benfica since joining the Lisbon club from Vasteras in 2012. He was a member of the Sweden U-21 side that won the Uefa European U-21 Championship in 2015.
United are in the market for a new striker after Zlatan Ibrahimovic suffered a serious knee injury towards the tail end of last season.
Real Madrid striker Alvaro Morata is reported to be Mourinho's priority transfer target, while Inter Milan winger Ivan Perisic has also been linked with a move to Old Trafford.