Lindelof will be United's first new signing of the close season.
United manager Jose Mourinho said Lindelof is a "very talented young player, " adding "our season a year ago showed us that we need options and quality to add depth to the squad".
"It would be a unusual summer if we weren't signing players like that".
The centre-back, who played 73 times for Benfica and earned 12 caps for Sweden, leaves the Primeira Liga side with three league titles, two national cups, a league cup and a Portuguese Super Cup to his name.
The Portuguese is again closing in on the Sweden global, though, with Lindelof set to add to United's defensive options next term.
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United are reported to have agreed a fee in the region of 35million euros, and the 22-year-old will complete his move to Old Trafford once he has agreed personal terms and passed a medical.
The Real Madrid forward's agent said earlier this week that United had lodged a "very important offer" with the Spanish giants to try to bring him to the north west of England.
It is still unclear whether Phil Jones and Chris Smalling have a future at United.
Lindelof began his career with Vasteras SK, and moved to Benfica in 2011. Everywhere you go you have to adapt to a new environment, but I feel comfortable in myself and I trust myself.
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