He did not name the exact type of cancer but said his recovery is taking longer than he had hoped.
He said: “The spirit has been more than willing but I have to now accept that it is going to take longer than I would have wished for me to recover my full strength
“Therefore, I must reluctantly cancel all the remaining engagements of this tour.”
Costello had been due to perform in Manchester last night and the remaining dates affected were for shows across Europe.
London-born Costello, son of a singer and musician with the highly successful 1940s Joe Loss Orchestra, said that at first his recovery had gone remarkably well but the strains of touring had proved too much.
He explained: “Six weeks ago my specialist called me and said he had rarely, if ever, seen such very aggressive cancerous malignancy defeated by a single surgery.
I was elated and relieved that our European summer tour could go ahead.”
But he added: “Post-surgical guidelines recommend three weeks to four weeks recovery depending on whether you are returning to a desk job or an occupation that involves physical work or travel.”
He said: “It was impossible to judge how this advisory would line up with the demands on a travelling musician, playing 90-minute to twohour-plus performances on a nightly basis.
By the time we reached the Edinburgh Playhouse, I was almost fooled into thinking that normal service had been resumed.
“I have to now accept that it is going to take longer.” The singer, whose hits include Oliver’s Army, She and Pump It Up, said: “My apologies go to our ticket holders but I would rather disappoint our friends by not appearing than press on with a show that puts my health.