Te size of the fee is undisclosed but Payero has signed a four-year deal with the option of a further 12 months.
The 24-year-old Argentinian midfielder was never able to make much impact on English football after joining from Banfield two years ago, and leaves with only 18 Boro appearances in all competitions to his name.
Payero spent last season on loan at Boca Juniors but it failed to turn into the permanent move Boro were hoping for.
So instead Payero has moved to Serie A Udinese, who pulled off one of the more surprising moves of deadline week by replacing Everton-bound Beto with Keinan Davis, who had been a Hull City target.
Payero's only appearance this season was in the League Cup win over Huddersfield Town.
His only goal for the Teessiders came in a 2-0 win at Cardiff City in October 2021.