From March, Bond will transport staff to and from the BW Offshore production platform, which is 110 miles (180km) north-east of Aberdeen.
A new AW139 helicopter will be used over the initial three years of the contract.
Shell excluded the operating company from a tendering process last May after a Bond-operated Super Puma EC225 helicopter carrying 14 passengers and crew ditched about 30 miles (48km) off the coast of Aberdeen. No-one was seriously injured in the incident.
It followed a disaster in April 2009 when a Bond-operated AS332L2 crashed in the North Sea, killing all 16 men on board.
RMT union leader Jake Molloy said Bond has a good safety record and the issue is with Eurocopter, the manufacturer of the aircraft.
"The issue is with Eurocopter, it's not a Bond issue, it's a manufacturing issue," he said.
"Bond's record stands up to everybody else's record over the last three years or so since the fatal incident, so I don't see why they should suffer any fall-out because of the current situation.
"The CHC helicopter that went down in October was the same issue, it's the design of the bevel gear shaft in the Eurocopter EC225, that's a fact."
In October last year, another EC225 helicopter, operated by CHC, ditched in the North Sea near Shetland and all crew were picked up by a passing vessel.
Bond is part of Avincis Group, a worldwide aviation firm.
Richard Mintern, the company's chief executive for Northern Europe and Asia Pacific, said: "This new win is the latest in a fantastic recent run of success for Bond, coming on the back of the new contract with Perenco in the southern North Sea, as well as contract renewals by long-standing air ambulance customers in Scotland and the Midlands.
"As it grows, Bond is also investing in staff and cutting-edge equipment, in order to continue providing the optimum level of service to its customers."
Bond also operates a fleet of search-and-rescue helicopters in the North Sea.
Last month it rescued eight crew men from the Vos Sailor, an oil rig emergency rescue vessel, which was taking on water.
The crew were winched from the ship and 10 workers were also evacuated from a nearby oil platform as the Vos Sailor drifted towards it.