Tech City Investment Organisation was set up in April 2011 to attract inward investment focused on an area in London's east End, dubbed "silicon roundabout" and supporting start-ups looking to expand.
It has signed up companies including Cisco, Google and Intel.
"The success of Tech City shows just what can happen when we back some of our most innovative and aspiring companies to grow," Prime Minister David Cameron said in a statement on Sunday.
Shields, will join TCIO in January, said she would lead a drive that hopes to make London the number one location for tech in the world.
Her departure will be a blow to Facebook, the world's biggest social network, as the U.S. group seeks to reassure shareholders after a rough reception on Wall Street since its high profile listing in May.
Concern about its slowing revenue growth rate has seen its market valuation halve - Facebook shares closed at $19.00 on Friday, compared with a $38.00 issue price in May.
"Facebook supports the UK Government's vision for building a stronger technology-based economy and start-up ecosystem, and we wish Joanna every success," a company spokesman said.
Earlier this week, Facebook opened an engineering centre in London, its first outside the United States.
© Thomson Reuters 2012
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