De Gea’s future has been up in the air in recent months as United tried desperately to keep him at the club in the long-term.
The Spaniard’s contract expires next summer.
But De Gea will soon pen a new deal which will see him become the world’s highest-paid goalkeeper.
The 28-year-old wanted parity with Alexis Sanchez, who currently earns £500,000-a-week at Old Trafford.
However, club officials weren’t willing to offer De Gea that much, instead giving £375,000-a-week to the stopper.
De Gea will put pen to paper once the first team return from their pre-season tour of Australia and the Middle East.
The five-year contract, if seen through all the way to 2024, will mean the former Atletico Madrid keeper has spent 13 years in England.
De Gea has previously been linked with moves to Real Madrid and PSG.
Los Blancos almost nabbed the Spanish No 1 in 2015 before a deadline day move fell through.
De Gea was tipped to replace Gianluigi Buffon at Juventus but a deal never materialised.
Speaking out over the United star’s future recently, Solskjaer was positive over the contract talks.
“David’s had a summer now where he’s been negotiating and thinking about his contract, so we hope that we’re going to get it sorted soon,” he said.
“I’m positive. Of course, with David, I’ve said many a time how lucky I am, and how happy we are, to have him in the goal.
“So we hope he stays here for many years.”
United have already tied Marcus Rashford down to a long-term deal.
Solskjaer has also strengthened his side by bringing in Daniel James and Aaron Wan-Bissaka.
Leicester defender Harry Maguire is the man United want to bring through the door next.