Engine Shed, close to Temple Meads train station, is home to dozens of growing technology businesses but needs to expand in order to offer support to more companies.
Initial plans for Engine Shed 2 could triple the amount of incubation space currently available for high-tech, social, creative and digital businesses in the Temple Quarter Enterprise Zone.
Mr Clegg revealed that £18.1million will be made available through the Growth Deal for the West of England LEP.
The new funding is an extension of the £214 million Growth Deal, which is money central government is handing over to local bodies to spend on projects to help the economy. Other projects also benefit in the latest announcement.
Some of the money will go towards providing 14,000 businesses with the chance to connect to super-fast broadband. And the rest will be spent trying to ease congestion at Aztec West roundabout, West Wick roundabout in Weston-super-Mare and Crow Lane roundabout on the A4018 near Cribbs Causeway.
Mr Clegg said: "A quiet revolution is under way in the West of England and across the country, as Growth Deals signal the death of the culture where Whitehall calls the shots.
"I've seen for myself the difference it makes to give the region more power over skills, over business support, over infrastructure spending. I am delighted to announce the expansion of the West of England Growth Deal today."
The Engine Shed, a Grade I listed building built by Brunel in 1841, had a £1.7 million transformation in 2013 thanks to a partnership between Bristol City Council, the University of Bristol and the West of England LEP.
It's managed by Bristol SETsquared - the University of Bristol's double award-winning business incubator - which has a third of the current space to provide premium serviced offices for its early-stage technology businesses.
Nick Sturge, the Director of Bristol SETsquared and Engine Shed, said: “We were pleased to welcome Nick Clegg back to SETsquared and to see our new home in Engine Shed. We now look forward to working with the LEP, Bristol City Council and the Government to deliver further growth, through Engine Shed 2, in the Bristol and Bath area.”
Mr Clegg was introduced to nine fast-growing, highly-successful SETsquared businesses - Neighbourly, Fusion processing, Systems4Silicon, BluWireless technology, Ultrahaptics, Kubla, FundSurfer, CameraForensics and IdeaSquares.