The agency won the account after a competitive pitch and will begin working with the brand immediately.
Agency Republic's appointment will strengthen its existing relationship with Danone. Earlier this year, the agency won the pitch for Danone’s Activia digital account. The company also owns Actimel, Volvic and Evian.
Shape has previously not had a dedicated digital agency.
Historically, Danone has not been a big spender on digital, but its "roller-skating babies" ad, created by Betc Euro RSCG, became one of the YouTube hits of 2009, with more than 45 million views in the six months after it launched.
In the UK, Danone’s above-the-line advertising is handled by Rainey Kelly Campbell Roalfe/Y&R.
Matt Kwiecinski, Agency Republic's managing director, said: "We are really pleased to be working with Shape. It is a fantastic brief and the Shape team has some big ambitions that they recognise we can help them achieve, through a progressive marketing agenda."
Danone's media planning and buying is handled by MEC.