The 32-year-old has been without a club since leaving Nottingham Forest in the summer and returned north of the border to train with Kilmarnock.
Killie boss Lee Clark insisted from the outset that his side couldn’t afford to sign the midfielder, who previously played under Clark at Birmimgham, but was happy for Burke to train with the Ayrshire side while he sought a new home.
County boss Jim McIntyre opened discussions with the player about moving to Dingwall and the deal was concluded this morning.
Burke previously spent nine years at Ibrox, having joined from Celtic boys club as a teenager, before signing for Cardiff City in 2009. He subsequently had spells at Birmingham, Forest and a loan spell at Rotherham United.
He has been capped seven times by Scotland, scoring two goals.