The keen drummer and member of Southgate Progressive Synagogue, who underwent a liver transplant in 1999 and a lung transplant in 2012, said: "I don't know how long I have left.
"Because of everything that has happened to me and now the cancer, I wanted to get married to Claire as quickly as possible."
The hospice staff organised a civil ceremony followed by a Jewish blessing performed by Rabbi Yuval Keren.
Mr Cooper said: "Claire is not Jewish but I wanted Judaism to be part of my wedding and so did she.
"It is part of my culture and religion and it was really important to me. The hospice was amazing. We got a lot of stuff donated, like the flowers and Claire's dress."
Mr Cooper, who started a Friday night rock band at his shul, said he counts Spice Girl Emma Bunton as a friend who has come to visit him at the hospice.
He said: "It is really nice that people have given up the time to see me."
Although her wedding day was not as she had "ever expected" Mrs Cooper described it as "perfect".
She said: "We planned to get married next December but because of the cancer I didn't want to wait. The doctors also told us to bring it forward.
"It was perfect. We got married in the hospice but you would never have known because they made the venue look amazing."
Mrs Cooper, who works as a support worker, moved to London from Oxford a year after the couple met.
She said: "He has fought all his life, and I think he is just amazing. I knew he was the one.
"Having the Jewish blessing was very important to me because it is part of his belief system.
"He has lost so much control in his life over his health - I thought it was important he had the control over the wedding and had the right to choose that he wanted it to be Jewish."
Rabbi Keren said although he does not "normally perform blessings for mixed faith couples", he felt "honoured" to do one for his congregant.
"Simon has always been a member of the shul and has always known his time was limited. He is a very determined man and a gifted musician.
"I went to see him and he told me he wanted to get married and wanted a Jewish blessing as part of the wedding. I felt honoured."
Rabbi Keren, who has been at Southgate for four years, said he could not deny Mr Cooper his wish.
He said: "I've never offered mixed faith blessing in the past, but Simon's contribution to our religious life at the shul has been tremendous.
"It was fitting to give him what he wanted because he is committed to Judaism.
"I was happy they picked me to bring God into their relationship. They know the future for them does not look good."
Rabbi Keren performed the blessing in front of a gathering of the couple's family and friends.
Mr Cooper's friends in Israel also watched a live stream of the ceremony.
He said: "The blessing is in some ways based on what you have at a Jewish wedding. There is no chuppah or the vows.
"But I read a passage from the Song of Songs and it was very difficult to read because it speaks about love being as strong as death.
"Simon stepped on the glass. It was sad but also very happy and powerful."
Chas and Dave - who regularly visit Mr Cooper - performed a special version of their song London Girl at the reception, changing the lyrics to "Oxford Girl" in honour of Mrs Cooper.
Pam McClinton, chief executive of the North London Hospice, said: "We are delighted to have been able to support Simon and Claire's wish to be married here at the hospice.
"That we were able to make it happen so quickly is a real testament to the collaborative spirit of the team here and our local community.
"It reflects the hospice's philosophy to achieve what is possible and focus on living."
Mr Cooper's mother, Angela, said: "It was a lovely day full of mixed emotions. We were very happy, but there was a tinge of sadness about what is to come."
