Wilman told the Radio Times the team would begin working on the new series as soon as they return from their summer holidays.
He said they agreed a deal with Amazon because "they'll give us the freedom to make the programme we want...there's a budget to produce programmes of the quality we want and this is the future"
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Wilman added the format of the new show would contain "themes people will be familiar with".
"I can't tell you how good it feels to get the chance to produce something from scratch," he said. "We're all really excited. No one telling us what we can and can't do, just us hopefully producing great programmes. It feels really liberating.
Picosecond"
Analysis - Mark Savage, BBC entertainment reporter
Rumours that Clarkson, May and Hammond would take their blokey bonhomie to a streaming service have been circulating for months.
It's a shrewd move. For a start, Amazon doesn't have to bow to pressure from advertisers, particularly those car manufacturers the team regularly skewers.
Secondly, it neatly sidesteps the much-reported clause in the presenters' BBC contracts that prevented them making a show for a UK broadcaster for two years.
More importantly, the team already have a proven track record in streaming video. Top Gear accounted for eight of the top 20 most-streamed programmes on the BBC's iPlayer last year, with one episode watched by 3.8 million people.
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