The Care Quality Commission (CQC) has rated as "good" Tameside and Glossop Integrated Care NHS Foundation Trust.
It was placed in special measures in 2013 and the CQC's 2015 report said this should be lifted although it "required improvement" in some areas.
The trust's chief executive said she was "proud" of the rating following the August 2016 inspection.
The hospital was placed in special measures after an investigation into high mortality rates at hospitals in the wake of the Stafford Hospital scandal.
The chief inspector of hospitals, Sir Mike Richards, said "it should be acknowledged how far they have come in three years".
Sir Mike added: "It is clear the trust has worked hard to address the issues we raised, and I am pleased to be able to change its rating from 'requires improvement' to 'good'."
Sir Mike said the inspectors found a "number of areas of outstanding practice" including:
â€¢ A programme for supporting pregnant women with alcohol problems
â€¢ The radiology department's virtual post-mortem examination service where a CT scan could determine the cause of death
â€¢ The trust's direct access to electronic information about patients needing end-of-life care.
But the report also said the trust must ensure there were enough nurses to meet patient needs, medication fridges must be kept at the required temperature and at least one nurse each shift on the children's ward should be trained in advanced paediatric life support.
Trust chief executive Karen James said she was "immensely proud" of her staff, adding: "Our journey will never be complete, we will continue to improve the quality of services at the organisation."
BBC analysis has found, however, that its bed occupancy is 98% - 13% higher than the NHS's recommended safe level.

Police say 540,000 people rallied in Barcelona, the capital of the region in north-east Spain, while the rest gathered in four other Catalan towns.
But numbers were down sharply compared with last year's event, when 1.4 million rallied in Barcelona alone.
Spain has consistently blocked attempts to hold a referendum on secession.
Catalan regional president Carles Puigdemont had urged support for "converting Catalonia into an independent state".
Divisions have also emerged between the separatist movement's main political grouping in the Catalan parliament, the Together for Yes coalition, and its radical leftwing ally, the CUP.
Mr Puigdemont, who took power in January, faces a confidence vote on 28 September.
He advocates a negotiated withdrawal from Spain.
When Catalan nationalists held an unofficial referendum on independence in November 2014, 80% of those who voted backed independence.
Sunday is the "Diada", Catalonia's national day. It commemorates the moment in 1714 when Barcelona fell to troops loyal to Spain's King Philip V during the War of the Spanish Succession.
"We have to move towards the final outcome," 58-year-old office clerk Xavier Borras, who planned to attend the rally in Barcelona with a friend, told AFP news agency.
"We can't wait any longer."
Spain's leading parties, deadlocked in their efforts to form a new government after two inconclusive general elections since December, have shown little sympathy for Catalan grievances.
The region of 7.5 million people makes up 16% of Spain's population and accounts for almost 19% of national GDP.
A health watchdog has praised the improvements at a hospital that was once placed in special measures.
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Some 800,000 people have turned out in Barcelona and other towns in Catalonia on a day of rallies by nationalists wishing to break with Spain.