All commercial flights of Super Pumas were suspended after a Super Puma AS332 L2 plunged into the North Sea off Shetland, killing four passengers, on Friday August 23.
The chopper, operated by CHC Helicopter, was carrying 16 passengers and two crew from the Borgsten Dolphin oil rig to Sumburgh airport in Shetland when it dropped out of the sky without warning, claiming the lives of George Allison, 57, Sarah Darnley, 45, Duncan Munro, 46, and Gary McCrossan, 59.
However, the Civil Aviation Authority said there were no grounds to continue the flight ban after initial investigations suggested the crash was not caused by a lack of airworthiness or a technical flaw.
The helicopter's "black box" flight recorder was recovered from the seabed on Thursday. It is hoped it will shed light on events running up to the fatal ditching.
The go-ahead for flights to resume comes amid calls for an emergency debate at Holyrood on offshore safety and criticism over delays in holding a fatal accident inquiry into a previous Super Puma crash in the North Sea in 2009, which killed 16 people.
A spokesman for the CAA said: "Based on all the information currently available, we do not believe that the accident was caused by an airworthiness or technical problem, and consider that the decision by the operators to resume Super Puma flights is appropriate. We would not allow a return to service unless we were satisfied that it was safe to do so."
CHC Helicopter said it had no immediate plans to alter its schedule, while another operator, Bond, said it would reintroduce its fleet of Super Puma AS332 Ls to non-passenger operations.
However, a third operator, Bristow, said it intended to resume services using the aircraft in the coming days.
Bob Crow, general secretary of the RMT transport union, said he supported the decision to return the Super Puma to operation.
He said: "We've got to look at the evidence that was put in front of us and at this moment in time there's no reason why the crash was mechanical."
Richard Baker, Labour MSP for North-East Scotland, has tabled a motion in the Scottish Parliament urging MSPs to debate the issue of offshore safety as soon as possible after parliament returns next week.