The agency scooped the business following a final shoot-out against Wieden & Kennedy Amsterdam. Euro RSCG and Ogilvy Advertising were knocked out earlier in the process, which was handled by the AAR.
The agency will be responsible for producing Dyson's above-the-line advertising across ten European markets, including Germany, France, Spain, Holland and Italy.
The appointment will not affect Dyson's relationship with VCCP, which currently handles UK advertising. Media, which is handled by MindShare, is also unaffected.
The campaigns will encompass television, print, press and online advertising promoting Dyson's range of products to both established markets and those European countries where the company has yet to forge a presence. The focus of the advertising will be on highlighting the vacuum cleaner's bagless features and high suction levels.
Tim Delaney, the chairman of Leagas Delaney, said: "We fought to get on the pitchlist and we fought to win it because we believe in Dyson as a company and its ethos.
"We are naturally very pleased with the outcome and are looking forward to working with the team."