Howe, 43, takes charge of a side languishing second from bottom of the Premier League, five points from safety, and without a win all season.
He replaces Steve Bruce, who left the club by “mutual consent” on October 20, two weeks after the Saudi-led takeover propelled the club into the ranks of the super-rich.
Newcastle said Howe, who was not first choice, had been handed a contract “until summer 2024”.
“We have been incredibly impressed by Eddie through what has been a rigorous recruitment process,” said co-owner Amanda Staveley.
“As well as his obvious achievements with AFC Bournemouth, where he had a transformational impact, he is a passionate and dynamic coach who has clear ideas about taking this team and club forward.”
Howe said it was a “great honour” to take the helm at a club with the stature and history of Newcastle, who have not won a major trophy since 1969 despite a huge and passionate fanbase.
“This is a wonderful opportunity, but there is also a lot of work ahead of us and I am eager to get onto the training ground to start working with the players,” he said.
Former England and Newcastle forward Alan Shearer welcomed Howe, tweeting: “Good luck Eddie. We all hope you can bring us some much-needed drive and ambition.”
And Newcastle United Supporters Trust chairman Greg Tomlinson hailed the appointment of a “progressive, modern manager”.
“A big challenge to stay up but our long-term future is bright,” he tweeted.
Newcastle’s new owners had to pivot towards Howe after Villarreal boss Unai Emery turned down an approach to be Bruce’s successor.
The former Arsenal manager was reportedly wary of joining the project in its infancy without a clear structure of how to make their new wealth pay on the field.
Newcastle - now one of the richest clubs in the world - are expected to invest heavily in the January transfer market.
But they have another nine league games to navigate before then, including daunting clashes with Liverpool, Manchester City and Manchester United.
Just staying in the lucrative top flight this season would represent success for Howe after an unsettling month for Newcastle fans since the Saudi sovereign wealth fund bought an 80% stake in the club.
Governor of the Saudi Public Investment Fund (PIF) Yassir Al-Rumayyan was in attendance for a 3-2 home defeat to Tottenham last month in the first match since the takeover.
Bruce left the club days later but Newcastle have continued to struggle under caretaker boss Graeme Jones, taking just two points from their past three fixtures.
Howe, who had two spells at Bournemouth, has been out of work since leaving the club in August 2020, days after their relegation from the Premier League.
The south coast club had risen from the fourth tier to become an established top-flight team under Howe.
The new manager’s first game in charge of Newcastle will be at home to struggling Brentford on Nov 20, following the international break.