The Scottish Premier League concluded that neither club had a case to answer in respect of their responsibilities and that Hearts' stewarding arrangements were entirely consistent with both the club's Safety Certificate and the requirements of the police.
Two fans were arrested at the fixture, one of those the spectator who made his way from his seat in the main stand to reach the Celtic technical area unhindered during their match at Tynecastle on May 11.
The SPL statement read: "The SPL Board recently received a report following the Heart of Midlothian v Celtic match on Wednesday 11 May 2011. The Board also considered the reports from the SPL Match Delegate and the Match Referee.
"The SPL Board noted that Heart of Midlothian identified the fixture as a high-risk game and in addition to the usual pre-operations meeting between the clubs, Lothian and Borders Police and G4S, Heart of Midlothian had arranged an earlier meeting with Lothian and Borders Police to specifically discuss safety and security aspects of the game.
"The SPL Board also noted that Heart of Midlothian's stewarding arrangements were entirely consistent with both their Safety Certificate and the requirements of Lothian and Borders Police. In accordance with these requirements, a steward was deployed to each gate at half time and full time, but not during the match. The Heart of Midlothian Safety Certificate is provided by the Safety Committee of City of Edinburgh Council.
"The individual alleged to have assaulted Celtic Manager Neil Lennon is being dealt with by the justice system and has been give a life ban from Tynecastle Stadium by Hearts.
"G4S stewards, employed by Heart of Midlothian, sought to challenge offensive singing amongst both sets of fans when it occurred and correctly challenged other incidents of disorder.
"The SPL Board noted that both clubs implemented fully the Guidance for Clubs on Unacceptable Conduct issued by the SPL in 2007 to aid full compliance with SPL Regulations in this area.
"The SPL Board decided that no action should be taken against either club as the action taken by each club before, during and since the match was reasonable in all the circumstances."