The agency won the business following a four-way pitch against Beechwood, Albion and the incumbent, Isobel, which pitched with undisclosed partner agencies.
The winning agencies will work on establishing the Danish brand following its launch in the UK last August.
Barry Cook, the founding partner of Krow, said: "We're delighted to have won this business. From the moment we got involved, we were excited about how different the ILVA proposition was, and we relish the opportunity to bring this difference to life and establish the brand in the UK."
Pippa Wicks, the executive chairman of ILVA, added: "We were really excited about the combination of creative and practical ideas that Krow could offer us."
ILVA is backed by Advent International, a private equity group, which bought the company for a reported £67 million in 2003.
In December 2005, Isobel created a launch campaign for ILVA's first three UK megastores, in Thurrock, Gateshead and Manchester.