The broadcaster ordered a six-part run of the show after being impressed by a pilot made during the BBC's Salford Sitcom Showcase last year.
The project, based on the life of stand-up comedian and show creator Jason Cook, focuses on Jason, who leaves Tyneside to move to Manchester.
Jason has secretly married a Jewish girl called Clare and comes to realise that he needs to introduce her to his family.
Reeves will star in the show as Jason's father Tony, while Fresh Meat's Kimberley Nixon will play Clare.
Stand-up comedian Chris Ramsey has landed the role of Jason, while Cook himself will play a character based on Ramsey.
The BBC's executive editor of comedy commissioning Kristian Smith said: "We are delighted to be bringing Hebburn to BBC Two. Not only does it bring back the warm heart of the North East to sitcom, but also delivers a charming and funny comedy about a grown up family with a fantastic cast attached."
Other projects currently in the works for BBC Two include drama Top of the Lake - which stars Elisabeth Moss, Holly Hunter and Lucy Lawless - and thriller The Fall, which features Gillian Anderson.
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