"Shortly after I left Everton last summer I made certain accusations which I do now regret due to a basic misunderstanding," Stubbs told Evertons official website.
"I suggested that the club was unwilling to remove from the 12-month contract extension I had been offered a clause that may have had a bearing on that deal if there was to have been a recurrence of my cancer.
"I now accept that, as the club said at the time, they were fully prepared to remove the clause in question upon my being given the all clear by a specialist.
"I appreciate that, at the time, my comments may have caused offence to some people; I can only apologise. It was a difficult time for me and with the benefit of hindsight I accept that I misinterpreted certain information, which had been given to me by the club.
"I am absolutely thrilled and delighted to be back at the club I have supported all my life. What happened last summer is now water under the bridge.
"My target is now a simple one. I want to prove my worth between now and the end of the season in the hope of securing a contractual extension.
"All I want to do now is play for Everton for as long as possible and to end my playing career at Goodison Park."