The UK Civil Aviation Authority (CAA) and the Norwegian authorities have allowed flights to resume if operators meet new safety conditions.
A crash involving the helicopter off the coast of Norway killed 13 people, including Iain Stewart from Aberdeenshire, in April 2016.
The Unite Union has expressed concern about the decision.
CAA head of airworthiness John McColl said: "This is not a decision we have taken lightly. It has only been made after receiving extensive information from the Norwegian accident investigators and being satisfied with the subsequent changes introduced by Airbus Helicopters through detailed assessment and analysis.
"The safety of those who travel on offshore helicopter flights is a key priority for both the UK and Norwegian aviation authorities.
"We would not have made this decision unless we were convinced that the changes to the helicopters and their maintenance restore the required airworthiness standards."
The CAA said that helicopters would not begin flying immediately. A plan of checks, modifications and inspections will be undertaken before any flights take place.
These include:
Mr McColl added: "We continue to work with the helicopter operators, the offshore industries, international regulators, unions and pilot representatives to enhance offshore safety standards still further and all these parties are actively involved in ongoing discussions."
The Unite Union has expressed concern at the decision, saying its members were "very nervous" about flying in the helicopter.
The union's regional organiser in Aberdeen, Tommy Campbell, said Unite was still waiting to see a full analysis of the April 2016 accident and its causes.
"The offshore work force have been surveyed, they've been surveyed by the unions, they've been surveyed by magazines in the industry and there is a lack of confidence," he told the BBC.
"There's a significant issue and it's very understandable. Offshore workers - or any workers - want to go to their work and come back home safely and there's been far, far too many deaths now as a result of helicopter accidents."
Les Linklater, executive director of the offshore industry safety group, Step Change in Safety, said: "At this time, there is an ongoing Airbus survey for pilots and passengers regarding these specific helicopters' flight safety and comfort, which was issued just one week ago. It's our understanding that this survey still has a further three weeks to run.
"Given the importance of the workforce's opinion regarding this highly emotive subject, we do not feel it's appropriate to make any further comment until Airbus has gathered, and shared, the survey's results and can demonstrate how they intend to address any concerns raised by the workforce.
"We would encourage all members of the workforce to participate and have their voices heard."
Super Puma 225 helicopters, which were grounded after a fatal crash in Norway, are to fly over the North Sea again.