The agency picked up the comms planning and media buying for the clothing retailer without a pitch.
Its first work for the brand will be to oversee its autumn/winter campaign, which is due to break later this summer.
The campaign will include press, digital and outdoor activity, as well as PR and partnership marketing work.
It will be devised by Jigsaw's in-house creative team and shot by Bryan Adams, the Canadian rock star who sidelines as a fashion photographer.
Jigsaw has more than 40 UK stores and also sells its products in some department stores such as John Lewis.
Adam & Eve and the7stars launched Eden in January as a joint venture, with each agency taking 50 per cent of the profits. The start-up began life with the £10 million Phones4u media business as its first client.