His new deal will run until 2025, earning the Spain goalkeeper more than £110million over six years.
De Gea will sign the £375,000-a-week deal, when the club return from their pre-season tour.
He was previously earning around £240,000 weekly at Old Trafford.
The fresh terms make De Gea the highest-paid keeper in the world.
The 28-year-old would have been a free agent next summer, amid interest from Paris Saint-Germain.
De Gea joined Manchester United from Atletico Madrid in 2011 and has gone on to win a Premier League title, an FA Cup, a League Cup and three Community Shields domestically, to go with a Europa League title in 2016/2017.
