Howe watched from the stands as Newcastle drew 1-1 at Brighton on Saturday, making them the only winless side in the Premier League this season.
Newcastle United co-owner Amanda Staveley said: “We have been incredibly impressed by Eddie through what has been a rigorous recruitment process.
“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.
“He is a great fit for what we are trying to build here. We are delighted to welcome Eddie and his staff to St James’ Park and very much look forward to working together towards our collective ambitions.”
Newcastle said an announcement on first-team coaching appointments will “follow in due course”.
Howe will have the international break to work with his players who are not on duty with their countries, before promoted side Brentford head for Tyneside for his first fixture on November 20.
There will be a series of familiar faces in the dressing room – striker Callum Wilson and midfielders Matt Ritchie and Ryan Fraser all worked under him during his time with the Cherries.