Previously sales and marketing manager for design agency Brand/68, Ms Swindell, 27, is a graduate of Cardiff University and has since worked in event management.
She has specific experience of the financial services sector.
At Spindogs, Ms Swindell will assume responsibility for the management of key client accounts while also being involved in business development alongside director Liam Giles.
Mr Giles said: "Despite the economic climate, we have enjoyed strong growth over the last year and are confident that 2011 is proving to be another successful year.
"Claire's appointment is a reflection of our confidence in the future and our commitment to developing great websites and online marketing campaigns for our clients that are backed up by strong customer service."
Established by directors Mr Giles and Elwyn Davies in 2005, Spindogs employs a team of 13 and is expected to turn over £600,000 in the current financial year.
The team has won a series of prestigious UK-wide tenders and been appointed to deliver websites for Sony, Plaid Cymru, Milford Haven Port Authority, Atlantic College and McLays.