The former Little Britain star, 46, replaces Sandi Toksvig and will present alongside Noel Fielding.
He will join the flagship Channel 4 programme when filming for the 11th series begins in spring.
Lucas said: "I'm chuffed to bits to be joining the most delicious show on television.
"I can't wait to break bread with Noel, Prue and Paul and meet the brilliant bakers.
"And bearing in mind my love of cake, I've already ordered some much larger trousers in anticipation. See you in the tent."
Fielding said: "I love Matt. I love his warmth and his comedy and his big joyful smile.
"I think if we play our cards right we could become the next Chas and Morph."
Toksvig, 61, announced her departure from the show in January, saying she wanted to spend more time on her other work.
Jo Brand, Nadiya Hussain, ex-Bake Off contestant Liam Charles and comedian Sarah Millican were among the bookmakers' favourites to replace Toksvig.
The British Bake Off Twitter account shared a video of Fielding giving his new co-host a lesson in how to introduce challenges in the tent.
"The judges want you to make 24 yeasted festival buns," Lucas says, reading from a card, before adding: "I have a lot of work to do."
Lucas also shared a photo of Marjorie Dawes, who he played in Little Britain, captioning it: "mood."
Dawes, the cruel leader of a local FatFighters group, was known for bullying attendees about their weight.
Responding to the news, judge Paul Hollywood said: "I'm a genuine fan of Matt's, it is such great news he will be joining us in the tent, he's a fantastic addition to the team."
Co-judge Prue Leith said: "The combination of Matt Lucas and Noel Fielding - will we stop laughing and get any filming done?"
Chief executive and executive producer of Love Productions Richard McKerrow said: "It's extremely exciting to have Matt joining the Bake Off family, he's a phenomenal talent with a huge heart and we can't wait to enjoy the mischief and mayhem he and Noel will inevitably create in the tent.
"Our new batch of bakers will be in very safe hands."
Channel 4's director of programmes Ian Katz said: "We're thrilled that one much-loved national institution is joining another.
"Matt has everything it takes to be a great Bake Off presenter - he's warm, hilarious and loves cake."