The 22-year-old is well accustomed to the Championship having spent last season on loan at Bristol City, keeping 14 clean sheets and conceding 54 goals in 41 league games.
Vitek made it well known that he was looking to leave Man United in search of first-team football this summer.
"I feel great and ready to go again somewhere to be, hopefully, number one, so we will see. We will see what is going to happen," the goalkeeper said after United's 1-0 pre-season defeat to Wrexham.
"At the moment, I am still here, but we will see," he added. "I hope there will be some interest. I think you will know when things are more concrete.”
Middlesbrough have no confirmed that Vitek has joined for an undisclosed fee and an undisclosed amount of time as they didn’t announce the length of contract he has signed.
"The project here is very impressive, because you can clearly see the ambition and where the club wants to go," he told the club website.
"The mission is clear: to go to the Premier League. I think everyone at the club has that mindset, and I want the same thing."