In the statement released by his representatives SEG on Friday, the former Ajax boss expressed heartfelt gratitude to the fans for their tremendous support.
"Thank you for always being there for the club," he said. "Whether it was at a game far away or a tough match at Old Trafford, your support has been unshakeable.
"The atmosphere at Old Trafford has always been electrifying, thanks to you.
"I felt it many times. Also in away games, it gave the team and me an incredible feeling to hear the United chants taking over the opponents' stadiums, whether the game was in England, Europe or during the summer tours."
He also thanked staff throughout the club for their "unwavering support in good times and bad".
Ten Hag said he would "cherish" the trophies he won during his stint at Old Trafford.
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"Of course, my dream was to bring more trophies to the cabinet," he said. "Unfortunately, that dream has come to an end.
"I wish all Manchester United fans nothing but success, trophies and glory. Your support and the warmth I received from everyone at the club helped me feel at home. Thank you for this chapter in my life. Erik"
Ten Hag was fired after Sunday's 2-1 defeat at West Ham, which left United 14th in the Premier League.
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Interim boss Ruud van Nistelrooy oversaw a 5-2 League Cup win against Leicester on Wednesday and is now preparing to lead the side in Sunday's league game against Chelsea.
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(Except for the headline, this story has not been edited by staff and is published from a syndicated feed.)