The Daily Telegraph claimed Black had advised undercover reporters how to bribe officials at other clubs.
During an internal investigation, Southampton requested the Telegraph provide them with evidence.
In a statement, it said: "There is no evidence of any wrongdoing, as such the club now considers the matter closed."
The statement added: "Despite numerous requests to provide the club with any evidence relating to the allegation against Mr Black, none has been forthcoming. "
Black, 54, joined the Premier League club in June as assistant to manager Claude Puel.
The former Aston Villa caretaker manager and Aberdeen striker denied the allegations.
Southampton have concluded there is "no evidence" to support allegations of wrongdoing made by a newspaper against its assistant manager Eric Black.