The Tech City Investment Organisation (TCIO) supports firms based near the Silicon Roundabout area of east London.
Ms Shields will replace current head Eric Van Der Kleij in January 2013.
“Joanna’s experience will be hugely valuable in supporting Tech City as it goes from strength to strength,” Prime Minister David Cameron said.
“The success of Tech City shows just what can happen when we back some of our most innovative and aspiring companies to grow, helping the UK compete and thrive in the global race.”
Ms Shields has been Facebook’s vice-president and managing director of Europe, Middle East and Africa since 2010.
Prior to that she worked at Google and teenage-focused social network Bebo.
“Working in the UK for the past decade has proven to me that this country has the potential to become a major force in digital innovation,” she said.
“The seeds have been sown in east London for a dynamic and successful cluster: we have the infrastructure, the technology and the talent, now we need to accelerate the growth. I am looking forward to leading the Tech City Investment Organisation in the next phase of its development.
“With the right boost now, there is no reason why we can’t make London the number one location for tech in the world.”
Ms Shields will be seen as a key component if the UK is to encourage successful start-ups to begin trading on the stock market.
Unlike the US’s Silicon Valley – with the likes of Google and Facebook among its success stories – similarly aspiring companies in Britain have been reluctant to go public.
To aid in this, government adviser for technology Rohan Silva is leading efforts to relax the rules for financial listing and reporting. It is hoped making it easier for UK companies to go public will entice a greater number of foreign investors.
Companies such as Mind Candy, which runs children’s social network Moshi Monsters, and gig recommendation site Songkick are tipped as potential candidates to list on the London Stock Exchange.
The BBC understands that music-streaming service Spotify – which was founded in Sweden – is also among the firms the government is keen to encourage to begin trading in the UK.
TCIO was set up in April 2011 with the intent of raising the profile of UK technology companies, particularly the start-up scene.
Its role includes promoting the UK as a place for prospective entrepreneurs to move to in order to set up their own businesses.
However, the quango was criticised in June for operating in a way that was “potentially counterproductive”.
Think tank Centre for London raised concerns over skill shortages and rising costs of working in the area.
At social gatherings in the area, TCIO was regularly criticised for not publicising its events or services well enough.
To counteract this, the organisation hired Benjamin Southworth as deputy chief executive in July. Mr Southworth had previously been part of 3Beards, the group behind several key industry social events.