Lyrics on the rapper's first record in four years seemingly confirm the rumours that emerged following the release of his wife's critically acclaimed visual album Lemonade last year.
On the title track of the new album, Jay Z repeatedly apologises for past indiscretions , while on another, Kill Jay Z, he addresses the 2014 Met Gala where Beyonce's younger sister Solange launched herself at him in a lift.
On 4:44 he sings: "If my children knew, I don't even know what I would do.
"If they don't look at me the same I would probably die of all the shame."
More lyrics include: "I apologise, often womanise, took my child to be born, see through a woman's eyes. Took for these natural twins to believe in miracles. Took me too long for this song. I don't deserve you."
He also admits he "toyed with your emotions because I was emotionless".
Jay adds: "What good is a menage a trois when you have a soul mate?"
Liftgate - when Solange was caught on CCTV beating Jay in the Met Gala lift while Beyonce quietly ignored the drama just inches away - was also referenced in Kill Jay Z when he raps: "You egg Solange on knowing all along all you had to say was you was wrong.
"You almost went Eric Benet. Let the baddest girl in the world get away. I don't even know what to say, n****r never go Eric Benet."
The record, which is exclusively streaming on Tidal, features vocals from Beyonce as well as contributions from Frank Ocean, Damian Marley and the rapper's mum, Gloria Carter.
Fans on social media took aim at the musician over his confession, with one tweeting: "How dare Jay Z do that to Beyoncé?"
Another wrote: "If Jay Z can cheat on Beyonce (who's worth 500mil+) and openly acknowledge it. Y'all regular females getting cheated on #sorrynotsorry."
A third posted: "JAY Z CHEATED ON BEYONCÉ PEOPLE PERSCEUTED BEY FOR LEMONADE BEING FALSE BUT SHE WAS LETTING OUT HER PAIN!"
It comes just days after Beyonce gave birth to the couple's newborn twins, whose names and pictures have still not been made public.
