The 32-year-old, who can play in central midfield and across defence, is expected to go straight into the Clarets' squad for this weekend's Championship clash against Charlton Athletic.
"He's someone we've been keeping tabs on. He has experience and can cover a number of slots," Burnley manager Sean Dyche is quoted as saying by the Burnley Express.
"That experience can be very useful in any given occasion. If he's feeling well and he's right, we'll use him accordingly. He's played right back a lot and actually played there with a very young Sean Dyche at Watford.
"He can also play in midfield and can go a good job at centre-half if required and played a lot of games at the top level."
Baird previously made nine appearances for Reading this season - including a 2-1 defeat against Burnley in October - before leaving the club in January.