The famously flat-capped Cosmi, also a former Palermo boss among his many coaching jobs, failed to keep Lecce in the top flight last term but has been entrusted with doing better at a Tuscan side who excelled by finishing 14th.
Siena were fined 50,000 euros by the Italian football federation this month for their involvement in match-fixing and illegal betting while in the second division two years ago.
Cosmi's first task will be trying to cling on to striker Mattia Destro, with some of Serie A's top clubs inquiring about his services.
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