"The Burj Dubai reflects the ambitious vision set by His Highness Sheikh Mohammed bin Rashid."
Sheikh Mohammed had been "the first supporter of the company and all of its projects since its inception", he added.
Developer Emaar had planned to open the the iconic tower on December 2, Alabbar told CNN last month.
December 2 is the National Day of the UAE.
In the CNN interview, Alabbar said that he was "shooting for UAE National Day", adding that "12,000 staff were working inside trying to get the building ready".
Work on the Burj Dubai started in January 2004 and the tower reached 100 levels in January 2007. A month later, it surpassed the Sears Tower in Chicago as the building with the most floors in the world.