It is Vindel's first role since he quit as Band & Brown's deputy MD last August.
The new division was launched this week and is focused on winning software, hardware, infrastructure, mobile and security business.
Red Consultancy MD Andrew Baiden said: 'This is a real bid for B2B technology, which is a massive area for us to get into. We're going to build the whole thing around David.'
Vindel is expected to head a team of six, for which he will be recruiting.
At Band & Brown, he led teams on technology blue-chip clients BT, Cisco Systems, LogicaCMG, Reuters and Sony Ericsson.
He was also responsible for the agency's global network Bandwidth.
Red has also recruited Rainier PR director Paul Allen to its consumer tech team.