County chairman Peter Swanson told BBC Sport: "We were delighted at the quality of the applications we received to succeed Alex Smith.
"And this appointment shows Ross County's ambition to go forward to the next level."
Robertson, who started coaching with Livingston, was appointed manager of Caley Thistle on Boxing Day in 2002 and won promotion to the SPL in the following season.
The former Scotland striker, who still has a Highland home, left County's local rivals in November to become head coach of Hearts.
But he was dismissed after new major shareholder Vladimir Romanov decided he wanted a higher-profile manager at Tynecastle.
County sacked Alex Smith this month after the veteran former St Mirren, Dundee United, Clyde and Aberdeen manager failed to win promotion in his two and a half seasons in charge.
Former Scotland midfielder Asa Hartford had gone public with his interest in the job, while another former Caley Thistle manager, Steve Paterson, had also been linked with the job.
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