Clarke, 55, has left Kilmarnock to replace Alex McLeish, signing a three-year deal with the Scottish FA.
Brown, the last Scotland manager to lead them to a major finals, selected Clarke for his side in the 1990s.
"They need a bit of brightness and a slight uplift from the depression surrounding the team," he told BBC Scotland.
Clarke, the former West Bromwich Albion and Reading manager, was capped six times and had a year to go on his Kilmarnock contract.
"The players who have played for him respect him hugely," Brown said of the PFA Scotland and Scottish Football Writers' Association manager of the year, who has also held senior coaching positions at Newcastle, Chelsea and Liverpool.
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