Smith, 47, signed a two-and-a-half-year deal at Villa, taking him through until the end of the 2020-21 season after a very impressive start to the Championship campaign with Brentford.
Villa, on the other hand, lie way down in 15th place in the Championship table after picking up just three league wins in 11 games under Bruce before they suffered a 2-1 defeat against Millwall after Bruce's sacking.
The Midlands outfit have moved quickly during the international break and although sporting director Christian Purslow spoke to Thierry Henry, it was clear the Frenchman had other intentions - he has since joined Monaco.
Instead, Purslow took a liking to Smith who will now combine with Richard O'Kelly at John Terry at Villa in a bid to push the club back towards the top six of England's second tier.
The report claims that Smith, who was earning £300,000 a year at Brentford - or just under £6,000 a week - will more than triple his wages, taking him to around the £1million-a-year mark.
Smith, who has supported Villa all of his life, will take charge of his first game for the club against Swansea City on Saturday at Villa Park.
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