Memphis has arrived in France to put the finishing touches to his United exit, with the Dutch winger due to undergo a medical on Thursday.
The 22-year-old hasn’t featured for United’s first team since November after making just eight appearances under Jose Mourinho.
The deal includes several add-on payments, depending on Lyon’s Champions League qualification, plus a buy-back option if United choose to re-sign Memphis.
But if Memphis proves to be a success for Lyon, then United could recoup the majority of the £25m they spent to bring the Holland international from PSV Eindhoven in the summer of 2015.
Memphis - who was also a target for Everton and Nice - was a regular under Louis van Gaal last season, yet suffered from inconsistency and netted just two Premier League goals.
He will become the second major departure from Old Trafford this month after midfielder Morgan Schneiderlin joined Everton in a £22m move last week.