The former Watford manager joins the struggling Lancashire club after Eddie Howe chose to part company with the the Clarets to make a return to former side Bournemouth
The former Chesterfield, Millwall and Watford defender led the Hornets to a top-half finish in his one season in charge at Vicarage Road, before being replaced by Gianfranco Zola following the Pozzo family's takeover of the Hertfordshire club in the summer.
However, despite Burnley's disappointing start to the campaign that sees them languishing in mid-table, Dyche declared himself delighted to take on the role with the Turf Moor outfit.
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"I wasn't at home having the weekend to think about it. I decided instantly and we got on with things as quickly as we could, but things still need to be put into place contractually.
"I was at Cardiff on Saturday to have a look at that and it was finally great to get out with the players on Tuesday.
"This is a club in some kind of transition after a spell in the Premier League, but it is clearly a club that wants to build and move forward and I desperately want to be a part of that and make sure that we do that."