The 52-year-old had previously been assistant to interim boss Neil McCann and has now agreed a two-year deal as manager at the Caledonian Stadium.
Former boss John Robertson was recently confirmed as the club's sporting director ahead of the 2021/22 season following a spell on compassionate leave.
Dodds has held the post of No 2 at Dundee United, Queen of the South, Dundee and Ross County, and now steps up to the top job at Inverness CT.
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