The Take Me Out host and the former cricketer will take over from Matt LeBlanc, who earlier this year announced he was leaving the motoring show after four series.
McGuinness and Flintoff will join motoring journalist and racing driver Chris Harris in the main presenting line-up.
Rory Reid, the BBC Two show's previous co-presenter, will now host Top Gear's companion show, Extra Gear, along with Sabine Schmitz.
McGuinness said the Top Gear role is a "real honour and I'm thrilled the BBC have given me this opportunity".
He added: "To be hosting a show I've watched and loved from being a small boy is beyond exciting. Top Gear fans worldwide are a passionate bunch and I consider myself one of them.
"Now let's start up this Great British machine and see what it can do!"
Flintoff said: "It's not often you have the chance to do both of your dream jobs, but I'm now lucky enough to say I will have.
"I've always been passionate about cars and I'm so excited to be joining the Top Gear team."
Flintoff on his varied career after cricket - The big interviewHarris, who has been a lead host on Top Gear since 2017, said of his new co-stars: "They're both brilliant, natural entertainers - and their mischief mixed with the most exciting cars on the planet is sure to take the show to the next level.
"My dream job just got even better."
Friends star LeBlanc joined Top Gear in 2016, but announced his departure from the show earlier this year because of the demands of the role, and how much it keeps him away from his family and friends.
The American actor was a surprise addition to the Top Gear presenting line-up along with Chris Evans two years ago, following the departure of previous hosts Jeremy Clarkson, Richard Hammond and James May.
Clarkson was controversially fired from the show by the BBC after a 'fracas' whereby a member of the production team was physically assaulted in a row at the Simonstone Hall hotel in the Yorkshire Dales after a row about food.
He then continued hosting the show after Radio Two presenter Evans threw in the towel after just one series.
LeBlanc's final series as lead host will air in early 2019.
McGuinness and Flintoff will start filming their first series with Harris in early 2019, and it will debut later in the year.
Patrick Holland, controller of BBC Two, said: "This is a thrilling manoeuvre from the Top Gear team and I'm relishing what this trio will deliver.
"Both Paddy and Freddie love their cars but, more than that, they'll bring a new energy and competitive spirit to Top Gear.
"Chris Harris might have the greater car skills, but when it comes to the infamous Top Gear challenges, he's going to have to bring his A-game to have the beating of these two."