Howe, who has signed a contract until the summer of 2024, has not been in management since he left Bournemouth in August 2020 following relegation.
“This is a wonderful opportunity, but there is also a lot of work ahead of us,” Howe told Newcastle’s website.
He takes over with Newcastle 19th in the table, five points from safety after 11 games.
Howe watched Newcastle’s 1-1 league draw at Brighton on Saturday from the stands.
“I am eager to get onto the training ground to start working with the players,” he added.
“I would like to thank the club’s owners for this opportunity and thank the club’s supporters for the incredible welcome they have already given me. I am very excited to begin our journey together.”
The Magpies had approached Villarreal manager Unai Emery to take over as their new boss, but the Spaniard turned them down.
Newcastle co-owner Amanda Staveley said the club had been “incredibly impressed” by Howe through what had been a “rigorous recruitment process”.
She described Howe, whose first game in charge will be at home to Brentford on 20 November, as a “passionate” and “dynamic” coach.
“He is a great fit for what we are trying to build here,” added Staveley.
Bruce left Newcastle by mutual consent on 20 October, just 13 days after the Saudi Arabian-backed £305m takeover of the club was completed.
Graeme Jones has been in interim charge and the Tyneside club have drawn with Crystal Palace and Brighton as well as losing to Chelsea under him.
Howe took Bournemouth from the bottom of League Two to the Premier League, and kept the south coast club there for five seasons.
He will be familiar with Newcastle players Callum Wilson, Ryan Fraser and Matt Ritchie having managed the trio at Bournemouth.
‘A wise signing’
Former Newcastle striker Alan Shearer on BBC Radio 5 Live
They have a guy who knows the league, who knows what it is like in that position. He understands the league and what a big club Newcastle are and he will come back energised and it is a very wise signing.
Three players in there that worked with him at Bournemouth – not too sure how Fraser will react with his ending at Bournemouth, that could be an interesting handshake.
New owners, new manager – Newcastle’s hectic 33 days
7 October: The Saudi Arabian-backed £305m takeover of Newcastle United is completed, ending Mike Ashley’s 14-year spell as Newcastle United owner.
12 October: Amnesty International writes to Premier League chief executive Richard Masters requesting an “urgent” meeting on proposed changes to football’s takeover rules following Newcastle’s change of ownership.
17 October: Newcastle’s new era under Saudi Arabian-backed ownership starts with a 3-2 defeat in what is under-pressure boss Steve Bruce’s 1,000th game in management.
20 October: Manager Steve Bruce leaves Newcastle United by mutual consent.
21 October: Newcastle United’s new owners hold talks with former Roma manager Paulo Fonseca, who is among several candidates considered as Bruce’s replacement.
23 October: Newcastle draw at Crystal Palace, a match at which a banner criticising the Saudi Arabia takeover is displayed.
29 October: The Premier League agree to meet with Amnesty International, who want the owners’ and directors’ test to include rules on human rights violations.
30 October: Newcastle suffer a 3-0 home defeat against Chelsea under interim manager Graeme Jones.
3 November: Villarreal manager boss Unai Emery confirms Newcastle’s interest in hiring him as Bruce’s successor but goes on to reject the club’s approach.
4 November: Former Bournemouth boss Eddie Howe emerges as the favourite for the job.