The agency fought off Consolidated PR and Staniforth to win the business.
It will now attempt to make Moneyextra.com stand out from its competitors in a saturated but expanding market, which is dominated by Moneysupermarket. com, Gocompare.com and Confused.com.
The agency will stress that the website has been around since 1995 and will promote it as user-friendly and comprehensive. The site will also be redesigned.
Weber Shandwick will also deal with concerns that price comparison sites are misleading consumers. Most price comparison websites receive a commission when companies they review gain business. Consumer watchdog Which? recently suggested people might get better deals by going directly to the retailer.
Wealth management business AWD Chase de Vere recently sold Moneyextra.com to a group of independent investors. Winston Eavis, account director at Weber Shandwick who will lead the retained account, said the website will try to retain independence.
According to Which? the top comparison sites are Gocompare.com, Confused.com and Moneysupermarket.com. In April the three websites had a combined total of more than 6.5 million unique visitors.