Riverside boss Steve McLaren is expected to sign the 28-year-old Aussie international for around £4m in the next two days.
McLaren told Boro's official website: "I can confirm that Mark is at the club. He will be taking a medical and we will be looking to finalise details of a deal to make him a Middlesbrough player within the next day or two."
Viduka, who earns a reported £65k a week, joined Leeds from Celtic for £6m four years ago.