The rapper blasted the funnyman for having a "crazy" face and claimed he hadn't had as much sex in his life as he had after the late-night talk show host mocked the 'Blood on the Leaves' hitmaker's recent Radio 1 interview, in which Kanye boasted he was the number one rock star in the world.
He wrote: "JIMMY KIMMEL IS OUT OF LINE TO TRY AND SPOOF IN ANY WAY THE FIRST PIECE OF HONEST MEDIA IN YEARS.
"JIMMY KIMMEL, I DON'T TAKE IT AS A JOKE.... YOU DON'T HAVE SCUM BAGS HOPPING OVER FENCES TRYING TO TAKE PICTURES OF YOUR DAUGHTER
"JIMMY KIMMEL PUT YOURSELF IN MY SHOES ... OH NO THAT MEANS YOU WOULD HAVE GOTTEN TOO MUCH GOOD P***Y IN YOUR LIFE...
"YOU CAN'T PUT YOURSELF IN MY SHOES. YOUR FACE LOOKS CRAZY... IS THAT FUNNY?... OR IF I HAD A KID SAY IT WOULD IT BE FUNNY???
"SHOULD I DO A SPOOF ABOUT YOUR FACE OR YOU F***ING BEN AFFLECK...#NODISRESPECTTOBENAFFLECK #ALLDISRESPECTTOJIMMYKIMMEL!!!!
"I LIKE YOU, YOU KNOW ME, I WENT TO YOUR FAMILY'S WEDDING
"WHO YOU MADE IT CLEAR TO ME WASN'T YOUR FAMILY WHEN I WAS ON THEN PHONE WITH YOU 5 MINUTES AGO, YOU MANIPULATIVE MEDIA M*********ER.
"SARAH SILVERMAN IS A THOUSAND TIMES FUNNIER THAN YOU AND THE WHOLE WORLD KNOWS IT!!! (sic)"
Not content with a 160-word rant, Kanye also posted two images on his Twitter account mocking Jimmy.
He uploaded a picture of Jimmy, who was making himself smile with his fingers in the photograph, and the rapper wrote in block capitals over the top of the image: "NO GOOD P***Y"
Kanye also posted another picture of animated character SpongeBob SquarePants complete with the caption: "JIMMY KIMMEL FACE M**********ER"
But Jimmy, 45, hit back at the rapper immediately by making light of his rant in the opening monologue on his show 'Jimmy Kimmel Live' on Thursday night.
He quipped: "Did anyone else get a very angry phone call from Kanye West about an hour and a half ago? Just me? OK. I didn't know if he was mad at all of us."
Following a commercial break, he then explained to his audience he had spoken to Kanye on the phone earlier in the day, and the 'Flashing Lights' hitmaker told him his life would be "much better" if he publically apologised.
He said: "That was really the only choice - the other choice he gave was, 'My life ... your life is going to be much better if I apologise,' And then he started tweeting today. And I don't even know if I've seen some of these because they're happening as we speak.
"And by the way, he told me on the phone - and I swear to God this is true - 'I am the most powerful voice in media. I am Pac.' He said 'Pac' a few times to me. I guess he means Tupac.
"He said, 'You will never be able to show your face at a 14 year old's high school football game and be cool again!' He really is Pac. I mean that's right out of the Tupac playbook, isn't it?"