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Ainslie led Oracle Team USA to victory in last year's America's Cup and later formed Ben Ainslie Racing (BAR).
Red Bull's chief technical officer Adrian Newey will be available as an advisor to the project.
"BAR are really excited to be partnering with Red Bull Advanced Technologies (RBAT)," said Ainslie, 37.
"RBAT will apply its simulation and modelling skills to assist Ben Ainslie Racing in various areas of their campaign.
"We are in a unique position in this country, and this campaign is about assimilating the very best of British in design and engineering - RBAT epitomises this."
Earlier this year, four-time Olympic champion Ainslie said he wanted Newey involved in the America's Cup project having met the designer at the 2013 Abu Dhabi Grand Prix.
Newey designed the Red Bull cars which Sebastian Vettel drove to win the world championship in 2010, 2011, 2012 and 2013.
However, he is now combining his time in F1 with other projects, of which the America's Cup is one.
Sir Ben Ainslie will work with a division of the Red Bull Formula 1 team as he ramps up his bid to win the America's Cup with a British team.