The 25-year-old has agreed an initial one-month loan deal and is expected to face Luton in the FA Cup first round at the weekend.
Malaga signed for the Sky Blues in the summer from Nice, but made just two appearances and was made available for transfer following the arrival of Mark Robins at the Ricoh Arena.
Boro boss Kevin Wilkin told his club's official website: "Sometimes when a player comes to a club it does not work out initially.
"Joining Boro will give Kevin the opportunity to play in a tough and competitive league against some real quality players."
