The Christmas Day meals will take place in Manchester, Leeds and London after Mr Sissay, who is Chancellor of Manchester University, raised Â£38,000.
The poet, who was in a Wigan children's home from the age of 12 to 18, said he wanted to create happy memories.
A group of volunteers has sourced the venues, transport, food and presents.
The dinners are being provided for care leavers in the three cities who are aged between 18 and 30.
"At its most simple the Christmas dinner offers a memory so next year the person can look back and think I was worth something then," Mr Sissay said.
"Christmas Day actually exposes the inadequacies of a system which treats children as if they are a problem because that day the child stands alone thinking 'I must be a problem, I'm obviously not worth anything because there is nobody here'."
The 48-year-old said his own early Christmas memories were "without family in virtually empty children's homes with staff who didn't want to be there".
"You have this secret room inside yourself and as Christmas approaches you draw back to that room. Each time you hear or feel the nature of family you are reminded of what you just do not have."
Mr Sissay said he believes people continue to feel isolated at Christmas after leaving care.
The first Christmas dinner took place in Manchester in 2013 and was extended to a second city, London, in 2014.
The money has been raised through crowd funding.

The comic actor, also known for his TV shows with Ben Miller, said voicing the character was "about as close to a dream job as you could wish for".
Armstrong takes over from Sir David Jason, who voiced the eye patch-sporting "DM" in ITV's original series from 1981 to 1992.
Kevin Eldon will voice trusty sidekick Penfold, Terry Scott's old character.
"When I am recording the episodes, I'll be making sure that at all times my eyebrows are at least three inches above my head," joked Eldon, known for his appearances in Big Train, Nighty Night and other comedy shows.
Other cast members include Shauna MacDonald and Morwenna Banks, while Dave Lamb - the voice of Channel 4's Come Dine With Me - will take on the role of narrator.
The new series, which will initially run for 52 episodes, is due to be broadcast on the CBBC channel in 2015.
Armstrong's Danger Mouse will have more gadgets at his disposal than the original, among them a multi-purpose "i-patch".
The actor previously voiced an alien super-computer in Doctor Who spin-off The Sarah Jane Adventures and Professor M in the animated series Tooned.
"As a lifelong fan of Danger Mouse, I was ecstatic just to know that the show was coming back," the 44-year-old said.
"To be actually involved with the reboot and to be taking DM out to a whole new generation is about as close to a dream job as you could wish for."
"We're all genuinely bowled over to have Kevin and Alexander on board as Penfold and the mighty DM himself," said CBBC controller Cheryl Taylor.
"They are both funny and fabulously talented performers and... will ensure that the series' considerable comedy credentials are bestowed on a new generation of fans."

Johnson was found guilty of sexual touching but cleared of one charge relating to another sexual act following a trial at Bradford Crown Court.
The court was told the grounds for appeal had been lodged on Thursday.
The former Sunderland winger is in court awaiting sentencing.
Johnson previously admitted grooming the girl and one charge of sexual activity.
Judge Jonathan Rose previously warned him he faced a "substantial prison sentence".

10 January 2017 Last updated at 16:08 GMT
"We are now in for a period of direct rule and I really do regret that, I think what the people of Northern Ireland want is stability but that has all been thrown in to very sharp relief," said Arlene Foster.
Young people who have spent part of their childhood in care have been invited to special Christmas dinners by Manchester poet Lemn Sissay.
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Pointless host Alexander Armstrong will voice Danger Mouse when the much-loved cartoon hero returns to TV next year.
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Ex-England footballer Adam Johnson is to appeal against his conviction of sexual activity with a 15-year-old girl.
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Northern Ireland faces a "brutal" election following the resignation of Deputy First Minister Martin McGuinness, the outgoing first minister has said.