The Uruguayan's contract at former club Southampton expired at the start of this summer, and Boro have now moved to sign the man they had on loan last season.
Ramirez arrived at Southampton for £12m in 2012, but started just 23 games in his time at St Mary's and spent the 2014-15 season on loan at Hull.
The 25-year-old rediscovered his best form last season in a loan spell at the Riverside, scoring seven goals in 18 games on Teesside.