The 24-year-old spent part of last season at npower League One side Walsall but became a free agent when his short-term deal expired.
Ledesma, who enjoyed a loan spell at QPR in 2008/09, scored four goals in nine starts for the Saddlers and it was that impressive form which alerted Boro boss Tony Mowbray.
Mowbray recently told the club's official website: "Having watched him last year, we know he's a talented boy.
"He's a centre-forward who drops into midfield and links the play up well. He's left-footed and has a real work ethic."
Ledesma added: "I'm passionate about football and I love the game. I want to do well for the team, the club and the fans."
Mowbray is also running the rule over goalkeeper Jayson Leutwiler as he looks for a new number two.
With first-choice keeper Jason Steele away on Olympic Games duty with Team GB and current understudy Connor Ripley involved in the European Championships with England's Under-19s, Mowbray is keen to strengthen his hand.
The Teessiders have confirmed that 23-year-old FC Basle player Leutwiler is at the club's Rockliffe Park training headquarters to allow staff to assess what he has to offer.