Boro on Thursday announced the deal had been completed and it's reported to be for €13.5m plus another €1.5m in bonuses.
“The Dutch midfielder has gone back to play in Italy after just one game in the Championship," read a Boro statement.
“The move is a permanent one, with Atalanta re-signing the player they sold to us a year ago.
“De Roon, 26, made 34 appearances in the Premier League and two in the FA Cup in his one season on Teesside, scoring five goals, perhaps the most memorable of which was the late equaliser away to Manchester City in November.
“Due to a privacy clause in the contract, we are unable to release the fee involved.
“Everyone at MFC wishes Marten all the best for the future."