The Spanish goalkeeper has experienced highs and lows during his nine years at Old Trafford and believes that the club and the city of Manchester have left a lasting impression.
He told United's website: "It's wonderful to be here and, to be honest, I feel right at home in Manchester.
"I'm still the same person I am today but I'm much more mature now. I was coming to a massive club, [with a] different language, a different culture, everything was different and I matured a great deal.
"I've grown a lot as a player and I'm truly grateful for all these years that I've been here. It's been incredible."
De Gea has enjoyed success in the Premier League and Europa League during his time at United and hopes to enjoy more triumphs with the team in years to come.
He said: "I think you learn from your mistakes, you start to mature and life throws up difficult situations. You learn from them, from the bad times especially, and I think that's life.
"The years have gone by. There have been good times and bad times but I'm doing well now.
"I’m looking forward to the future, which will hopefully bring many more years. Being at a club like this, and at this level for so many years, isn't easy so I'm proud of that."