Bournemouth were relegated from the Premier League a fortnight ago after finishing the campaign in 18th place, leading to the resignation of Eddie Howe as manager.
Tindall was Howe’s assistant and will now make the step up to try and bring the Cherries straight back up at the first time of asking.
“It’s an honour and a privilege to be the manager of such a great football club,” the 42-year-old told afcbTV.
“Given the success of the club over the last 12 years, with Eddie in charge and me by his side, I'm not going to come in and rip everything up and start again. I would be a fool to do that.
“But I’m my own person with my own ideas and I will be looking to implement them as soon as we get back on the training ground.
“I know the Championship is a very tough league but my aim is to get this club back into the Premier League at the first time of asking.
“This is a challenge that I feel I’m ready for and one I’m looking forward to."
AFC Bournemouth owner Maxim Demin said: “Jason has played a huge role in this club’s success over the last decade and fully deserves to step up and become our new manager.
“While his knowledge of and passion for the club is unquestionable, he was the standout candidate for this role.
“He has huge enthusiasm for the project and great ideas to get the best out of a talented squad.
“This is the start of a new era for this football club and I’m excited about what the future holds.”
