Whitmarsh will work alongside Britain's most successful Olympic sailor whose team is attempting to earn the right to challenge holders Oracle Team USA at the 35th America's Cup in 2017.
Team principle Ainslie said Whitmarsh's expertise from a career spent in the high-tech world of car racing makes him the perfect fit for the world's most famous sailing race, often described as F1 on water.
"I'm delighted that Martin is joining us," four-times Olympic gold medallist Ainslie said in a statement. "When we first started to put together the plan for BAR, McLaren were one of the aspirations.
"So it's particularly appropriate to have one of the original architects of that model as our new CEO."
Whitmarsh, who spent 25 years at McLaren and succeeded Ron Dennis as team principal in 2009, will move to BAR's purpose-built base in Portsmouth in April.
"After 25 years at McLaren it's great to be able to turn my energies and experience to such an exciting sporting and technical challenge," he said.
"I hope my experience will help BAR in its aspiration for a sustainable business model, along with the clear goal of winning the America's Cup and bringing it back to British waters."
Adrian Newey, who worked as a designer with Whitmarsh at McLaren and is still with the Red Bull team, is also part of Ainslie's team.
Britain has never won the America's Cup since the inaugural race was held in 1851 off the Isle of Wight.
(Reporting by Martyn Herman; editing by Sudipto Ganguly)
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