The move for the Swedish centre-back, 22, is subject to him completing a medical and agreeing personal terms.
If the transfer is completed it will represent United's first foray into the transfer market during the close-season, with fee reported to be €35 million.
A United statement read: "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 further announcement will be made once the transfer is complete."
Lindelof moved to Benfica in December 2011 and has won three Primeira Liga titles, two Taca de Portugal trophies and the Taca da Liga during his time at Estadio da Luz. He was also part of the side that won the European Under-21 Championship with Sweden in 2015.
Manager Jose Mourinho was reportedly keen on bringing Lindelof to Old Trafford during the January transfer window, but the move is said to have been scuppered by Benfica's valuation of the player.
The Portuguese is again closing in on the Sweden international, though, with Lindelof set to add to United's defensive options next term.
Defence is an area that United have been keen to strengthen, with Marcos Rojo suffering a major knee injury in April, while the futures of Chris Smalling and Phil Jones have been unclear with Mourinho criticising the duo and fellow injury-hit defender Luke Shaw during the previous campaign.
United have also been linked with a swoop for Real Madrid defender Raphael Varane, who worked with Mourinho at the Santiago Bernabeu, although reports suggest a transfer could depend on goalkeeper David de Gea moving in the opposite direction.