The 28-year old Sierra Leone international will link up with the Canaries until the end of the Premier League season but could remain at Carrow Road if he impresses during his initial temporary spell.
"It is a very bittersweet day as I am excited to achieve one of my goals, which was to play in the EPL," Kamara said in a statement.
"Being such a positive person, I trust in this decision and am thankful for the opportunity to play at Norwich City through the end of their season. I am grateful for the coaching staff at Sporting and especially Peter [Vermes] for believing in me and helping me through this process."
Kamara becomes the second SKC player to join a top flight English club in January following Roger Espinoza’s move to Wigan Athletic earlier this month.