The This Is England star said it was "worth living" following an attempt to take his own life during a period of despair in his early 20s.
Graham tried to hide the marks of his hanging attempt with high-collar jumpers before the truth of his suicide bid came out.
Following the traumatic low point, the versatile star of Boardwalk Empire and Line Of Duty was supported by his future wife Hannah Walters.
Speaking on Radio Four's Desert Island Discs, the actor said they moved in together in south London after what was technically their first date.
Graham's time in the capital before this was marked by despair. He said: "I had a breakdown. Going to that big London to do it on your own.
"Then I went back home. They (his parents) were trying to see what was happening with me.
"I'll never forget the tears coming down both their faces.
"Then the next day I tried to hang myself. It was very calculated.
"I kicked the chair and I heard my Nana's voice. She shouted 'Stephen' and I thought I'd gone. I just came to, opened my eyes and the rope had snapped. Thankfully.
"I had to put on a high neck jumper. My mum kind of saw it. Then everything came out. Life was worth living thankfully."
Graham said that in the aftermath of his attempt, his friends and family rallied round.
Tearfully talking on the Radio Four show, he also credited the help of his future wife.
He said: "This is kind of where Hannah came into my life properly.
"She knew what had happened. She was always in close contact with my mum."
Graham said that after a long period of "just talking" they had not been on a proper date, something he eventually remedied when she was due to move to Spain.
He recalled: "We were waiting at New Cross train station and I said to her 'please don't go to Spain. I love you".
"She went 'I've been waiting for five years for you to say that'. The next day we moved in together."
The mixed-race actor said he suffered racist abuse on the streets of Liverpool, which his mother quickly put a stop to. He also revealed he was unsure of his place in the world as a mixed-race child.
He said: "I'm mixed race and that was kind of frowned up in those days.
"There were times growing up when I was slightly unsure where I fitted in.
"That n-word popped up when I was younger."
Graham has recently starred in the new Martin Scorsese crime film The Irishman alongside his acting hero Robert De Niro.
The full interview with Graham can be heard on Desert Island Discs today at 11.15am.