The review, handled by Freestyle Marketing, began in May, and initially involved eight shops. Target Direct Marketing, the incumbent, was not involved in the process.
The win means Tequila will now take up a retained position on the charity's communications roster.
It will work on strategic development for the BHF's fundraising activity, campaigns targeting supporter acquisition management, and retention and upgrade campaigns.
Unlike the BHF's ad agencies, Tequila is not expected to repitch for direct marketing projects. Instead, it will create all of the BHF's below-the-line fundraising work.
Douglas Graham, the head of supporter retention at BHF, said: "We are delighted that we'll be working with Tequila. Its clear understanding of our needs, as well as its 'Disruption' tool and approach to audience segmentation, showed us that it is the ideal agency for the BHF."