From January 5, 2013, the ex-Radio 1 DJ will present 6 Music's all-new Weekend Breakfast Show on Saturdays and Sundays from 7am to 10am.
Presented live from 6 Music's studios at BBC North in Salford, Hobbs's Weekend Breakfast will be a "lively, upbeat show - packed with the music she loves, and plenty of audience interaction".
It will act a "gateway to the network", showcasing the best of 6 Music's output across the week, as well as "top-flight guests", archive sessions, and features on books, films, arts and entertainment.
"For me, music is life. I'm so excited to join a family with such depth and diversity of knowledge, pure passion and ingenuity," said Hobbs in a statement.
"I look forward so much to the new challenge of creating a beautiful Weekend Breakfast Show which embodies the whole spirit of 6 Music, and allows me to explore some fascinating new radio terrain."
Hobbs left BBC Radio 1 in 2010 after 14 years at the station, to take up a teaching and mentoring post at the University of Sheffield.
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She returned to the airwaves last year as a presenter on Xfm, and was nominated for 'Best Specialist Show' at the Sony and Arqiva Awards 2012. She left the station earlier this month.
As well as radio presenting and teaching, Hobbs also worked on sound design for Darren Aronofsky and Clint Mansell on their Oscar-winning film Black Swan. The soundtrack was nominated for a Grammy.
As a touring DJ, she has played to huge crowds of 15,000 people at Sonar festival in Barcelona. She also curates the festival, among others.
BBC 6 Music head of programmes James Stirling said that he was "thrilled" that Hobbs has agreed to return to the BBC with 6 Music.
"Her knowledge and love of alternative music is legendary, as is her dedication to sharing it with others," he said.
"Weekend Breakfast is a great place to showcase her special qualities as a music broadcaster and she will be a very welcome addition to our team."
6 Music's Weekend Breakfast Show is produced by Wise Buddah.