Howe added: "After nearly five years of giving my life, heart and soul into the club with unrelenting energy, I feel that it is in the best interests of both myself and the club to step away, recharge and take a break.
"Although it's been incredibly difficult to make this decision, I know in my heart that it's the right one.
"It has been the privilege of my lifetime to have been the manager of Newcastle United."
Howe's coaches Jason Tindall, Graeme Jones, Stephen Purches and Simon Weatherstone will also leave St James' Park, as well as head of performance Dan Hodges.
Howe took charge in November 2021 and steered the Magpies to an 11th-placed finish that season.
In 2022-23 they qualified for the Champions League and did so again in 2024-25, as well as winning their first major domestic trophy in 70 years.
Last season the Magpies reached the Champions League knockout phase for the first time, losing to Barcelona in the last 16, but they lost 17 of their 38 Premier League games and failed to secure European football for next season.
"There have been so many incredible moments in our time here," Howe added. "From fighting relegation in our first season to the numerous unforgettable nights at St James' Park in the Champions League soon after. The progression was fast.
"Everyone came together, united and what a force we became. These are all memories that I will cherish for the rest of my life."
Howe's final match in charge was a 4-1 defeat by Bristol City at Ashton Gate in a pre-season friendly on Wednesday.
The Magpies have lost two key midfielders this summer - Sandro Tonali to Tottenham and Anthony Gordon to Barcelona, while Arsenal are chasing captain Bruno Guimaraes, who has made it clear he wants to join the Premier League champions.
Last summer, Newcastle spent in the region of £240m on new players, but Howe was left frustrated when Alexander Isak's drawn-out transfer saga ended with the Sweden striker joining Liverpool for a British record of £125m.
"I remain incredibly positive and enthusiastic about the future of Newcastle," said Howe.
"The club is in fantastic hands with a great leadership team and I have no doubt together, alongside whoever comes in to replace me, they will continue to deliver success on the pitch."
Newcastle's chief executive David Hopkinson added: "Eddie and his staff leave with the deep gratitude and respect of everyone at Newcastle United, and with a lasting place in the club's history.
"While we are naturally disappointed to see Eddie leave, we remain immensely thankful for everything he has done for the club."
