The clubs have agreed a fee for the 22-year-old Ivory Coast international and he has arrived in Manchester to complete the finer details of his move.
His representatives expect the deal to be finalised by Friday.
Bailly will become the first signing of Jose Mourinho’s reign as Manchester United manager and is regarded as one of the best up-and-coming defenders in Spain.
Villarreal have not stood in his way as they knew United were willing to give them a substantial profit on the £4.4m they paid to Espanyol in January 2015.
They hope to clear £25m profit from the deal after paying Espanyol a sell-on fee.