Stats Perform understands United will pay the Bundesliga club £72.9m (€85m) for Sancho, with no add-ons included within the deal.
It will make the 21-year-old the fourth most expensive signing in United's history behind Paul Pogba, Harry Maguire and Romelu Lukaku.
Sancho is currently on duty with England at Euro 2020, a factor that is likely to delay the transfer being finalised.
Jadon Sancho to Manchester United... HERE WE GO! 🚨🏴 #MUFC #Sancho— Fabrizio Romano (@FabrizioRomano) June 30, 2021
Done deal confirmed. Agreement reached between Manchester United and Borussia Dortmund.
€90m with add ons. Agents fee and personal terms agreed, contract until 2026.
Medicals pending - then it’ll be official. pic.twitter.com/VBto2JqbtK
But United manager Ole Gunnar Solskjaer will hope to have the former Manchester City youth team player among his attacking options for his team's opening Premier League game against Leeds United at Old Trafford on August 14.
Since joining Dortmund in 2017, Sancho has scored 50 goals and provided 57 assists in 137 appearances across all competitions.
He boasts a healthy shot conversion rate of 23.7 per cent and has created 217 chances from open play, with a further 65 from dead-ball situations.
Despite this, he has been restricted to a solitary six-minute substitute appearance by England boss Gareth Southgate at Euro 2020 ahead of Saturday's quarter-final against Ukraine in Rome.
United finished second in the Premier League last season but a penalty shoot-out defeat to Villarreal means they remain without a major honour during Solskjaer's reign – something he will hope Sancho's arrival can help to remedy.