It is a direct challenge to Theresa May, who has avoided even the suggestion of a leaders' debate so far, and Mr Corbyn had previously stated he wouldn't join a debate without the Prime Minister.
The Labour leader said: "It's very odd that we have an election campaign where we go out and talk to people all the time and the Prime Minister seems to have difficulties in meeting anyone or having a debate".
Britain votes in a parliamentary election on Thursday June 8.
There will also be a political calculation in seeking to make the PM look weak and "running scared".
"I invite her to go to Cambridge to debate her policies, debate her plans. and let the public make up their mind".
He said: "Those nearest to me and those loved ones everywhere have a totally unreasonable amount of pressure put on them, and they always have done, all of my life, and I have a great deal of sympathy for them and a great deal of thanks to give them all, every one".
"The Tories have been conducting a stage-managed arms-length campaign and have treated the public with contempt".
Broadcast live on BBC 1, the debate will be moderated by BBC News presenter Mishal Husain, a Cambridge alumna.
Cleveland fires 1 officer, suspends 2nd in Rice shooting
Cleveland has exemplified these problems because it has a well-known history of excessive use of force by police officers. He would later accuse Samaria Rice of being " economically motivated " when she criticized his handling of the case.
Corbyn, a 68-year-old peace campaigner, has been speaking at modestly-attended fringe rallies and demonstrations for decades.
Liberal Democrat leader Tim Farron, Ukip leader Paul Nuttall, SNP deputy leader Angus Robertson, Green Party co-leader Caroline Lucas and Plaid Cymru leader Leanne Wood will appear, along with a senior Labour politician. Michael Deacon in the Telegraph said Mr Corbyn's performance had shades of his shadow home secretary Diane Abbott when she could not recall how much it would cost to recruit 10,000 police officers.
There were 239,700 tweets sent about Corbyn - compared with 107,800 for the Prime Minister - over the 90-minute period, during which the pair were questioned by a studio audience and Jeremy Paxman.
Mrs May's speech in Wolverhampton comes amid reports campaign chief Sir Lynton Crosby has told her to refocus the campaign on the choice of who should oversee Brexit, after a number of polls showed Labour narrowing the gap.
But according to Baldwin, the narrowing in the polls is more as a result of failings in the Conservative campaign, including pinning so much on May as a "strong and stable" leader, which backfired because she was forced to perform a u-turn over a major policy on funding for elderly care.
The snap election pushes back the date of the next planned national election from 2020 - just after Britain is due to have quit the European Union - to 2022, giving May more time to put the exit deal in place and potentially reducing political risk over how the deal is implemented.
In 2015, the comic - who has 12 million Twitter followers - famously suggested voting was not worth it, but endorsed then Labour leader Ed Miliband at the last minute after interviewing him for his The Trews YouTube channel.
"The futures of our NHS and schools are at stake in this election", Mr Corbyn will claim.