The agency beat Miles Calcraft Briginshaw Duffy to the business after a final pitch.
M&C Saatchi had been involved at an earlier stage but did not make it through to the last two.
AMV will now be briefed to create an ad campaign, including global TV work, promoting the charity's forthcoming rebrand.
Unicef recently hired the integrated brand consultancy Circus to help it work on that repositioning.
The charity does not have an incumbent UK advertising agency, but instead has a roster of direct marketing and digital agencies to work on specific projects, which includes Rapp and Profero.
Rapp was added to the roster in May last year to work on its Inspired Gifts range.
The charity's most successful recent communications campaign was the "Tap Project". It was based on an idea that restaurants in New York would ask patrons to donate $1 (which can provide children with safe water for 40 days) for the tap water they usually enjoy for free. The campaign picked up a D&AD Pencil in 2008.
A week ago, AMV landed the Cancer Research UK business after a final pitch against DDB and MCBD. The week before that, it won COI's Identity and Passport Services account after a pitch against VCCP and CHI & Partners.
Unicef is an international charity that is dedicated to promoting children's rights around the globe.