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.

Charlie Hodgson converted Samuela Vunisa's try and added two penalties to give Sarries a 13-3 lead at half-time, with Tom Catterick replying.
Hodgson then kicked two penalties after the break either side of Nick Tompkins' score from close range.
Fly-half Hodgson added a breakaway try late on before Billy Vunipola's score in added time sealed a bonus point.
Saracens remained the only unbeaten team in Europe this season and recorded their 13th consecutive victory over Newcastle Falcons in all competitions.
With new England head coach Eddie Jones in the crowd at Kingston Park, the north London side had to wait to be sure of victory as a kicking battle in the first half made for a scrappy game.
Newcastle, still without a league win this season, put pressure on Saracens' defence in the second half, but despite going through the phases they could not trouble the visitors' line.
It was from a Falcons attack that former England international Hodgson, who will retire at the end of this season, got the third try of the afternoon on 78 minutes after intercepting a loose pass and racing clear.
With the home side attempting to get on the scoreboard themselves in added time, a turnover and breakaway from Ben Ransom eventually allowed Vunipola to add Saracens' fourth score of the afternoon in the fourth minute of added time.
Newcastle director or rugby Dean Richards:
"I've not spoken to Eddie Jones, but I would have thought a lot of our guys should be in with a shout for England in the future, especially our hooker George McGuigan.
"It was 13-3 at half-time after we gifted them a try and, when it was 23-3, we started to push, made mistakes and conceded those two late tries.
"We started to chase the game and that fell right into their hands.
"They have a huge kicking game and they are very accurate in what they do. It enables them to sit back and wait and in the end their accuracy was far greater than ours."
Saracens director of rugby Mark McCall:
"It wasn't the most attractive of games.
"Newcastle came with a kicking plan and I was pleased with the patience and energy we showed.
"We stayed with it until the end and proved it's very important to be able to bring impact players like Billy [Vunipola] off the bench."
Newcastle: Tait; Agulla, Powell, Socino, Watson; Catterick, Young; Vickers, McGuigan, Welsh, Robinson, Green, Wilson, Welch (capt), Latu.
Replacements: Lawson, Rogers, Vea, Botha, Hogg, Takulua, Willis, Harris.
Saracens: Goode; Ellery, Tompkins, Taylor, Wyles; Hodgson, Spencer; Barrington, George (capt), Figallo, Itoje, Kruis, Wray, Fraser, Vunisa.
Replacements: Saunders, Vunipola, Du Plessis, Rhodes, Vunipola, De Kock, Streather, Ransom.
Referee: Andrew Small.
Attendance: 5,200.
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Southampton have concluded there is "no evidence" to support allegations of wrongdoing made by a newspaper against its assistant manager Eric Black.
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Saracens returned to the top of the Premiership table after securing a late bonus point in their win at Newcastle.