Froome, who joined the team in its first year in 2010, is one of 10 riders to sign contract extension with Nieve joined from the now defunct Euskaltel-Euskadi.
"This has been an incredible year for me and I am delighted to finish it off by signing a new contract with Team Sky,” said Froome said, who won another four stage races in 2013 on top of the Tour.
"I have been with this team since the start and I know this is the right place for me to continue to grow as a rider."
Nieve finished 12th overall at the latest Tour de France and replaces Rigoberto Uran at the team, joining the already announced new members of Nathan Earle, Philip Deignan and Sebastian Henao.
“Everyone is excited to kick things off again in 2014 and we do so with what we believe is the most talented team in the world,” Team Sky performance manager Rod Ellingworth said.
“We have consolidated what is an incredibly strong group of guys over the winter. The team’s core remains intact and that’s important going forward.
“Everyone is committed to keep improving and we always look to provide the best environment for riders to do that.”
Ian Stannard, Peter Kennaugh, David Lopez, Luke Rowe, Salvatore Puccio, Danny Pate, Xabier Zandio, Sergio Henao and Chris Sutton all also signed contract extensions although Team Sky declined to release any information on the length of contracts signed.