Spice, a former performance director for the RFU, Great Britain and England Hockey and British Basketball, replaces Michael Scott, who departed after the London 2012 Olympics, in the role.
Meanwhile Furniss, who coaches Britain's most successful swimmer in Olympic history Rebecca Adlington, is named as the replacement for Dennis Pursley as head coach.
Both will begin their roles in April, three weeks after the British Gas International Swimming Meet in Leeds with the trials for this summer's World Championships taking place in Sheffield in June.
And Spice is confident Britain can build on their performance at London 2012, which saw them make 23 finals and claim three medals, two bronzes from Adlington and silver from Michael Jamieson.
"One of the key things that attracted me to the position is the great potential I see within swimming and based on the solid foundation in place already I believe we can build for an exciting future," he said.
"I'm delighted to be working with Bill. He has an incredible pedigree and I'm certain this partnership will provide the perfect match of strategic leadership and technical knowledge. I feel it's a team that can take swimming to a new level and achieve fantastic things."
And Furniss, who has helped Adlington win double Olympic gold at Beijing 2008 and double bronze at London 2012, is determined to convert more finalists into medallists at major international events.
"I'm looking forward to working with Chris and what I know to be both world-class coaches and world class athletes as we strive to deliver the podium results in Rio 2016," said Furniss.
"In Britain we have some of the best coaches and most talented swimmers in the world and my role will be to work with them and their programmes to achieve the small margins required to convert finalists into medallists.
"Chris and I have already met and shared our beliefs and views about what is required to move swimming forward. He has an excellent background in sport at the highest level and together we know where collectively we can make a difference."
© Sportsbeat 2013