De Gea has signed a new four-year contract with the option to extend that by a further year, ending long-term speculation over his future at the club.
“I am delighted that David has committed his long-term future to the club," Solskjaer said. "Over recent years, David has proved himself to be the best in the world and a vital part of our plans as we look to take Manchester United back to where it belongs.
"David is a fantastic person and his outstanding quality provides the perfect base to our defence.
“Over his time here, David has really understood the values of playing for Manchester United and now represents everything you want in a goalkeeper. As a player he is still hugely determined and hungry to achieve more. We all look forward to working together to meet those ambitions over the coming years."