Portal - who helped guide Chris Froome to four Tour de France titles - died of cardiac arrest, according to L'Equipe.
"It is with the greatest sadness that we announce the passing of our much loved team mate, colleague and friend Nico Portal who died suddenly this afternoon at his home in Andorra," the team said.
"We are all overcome with grief at this terrible news and would ask everyone to respect the family's privacy at this difficult time.
"RIP Nico - your spirit will always be with us on the road and you will forever be in our hearts."
Portal was a former rider who retired in 2010, after one season with Team Sky, having missed much of the previous year because of heart problems.
Following the departure of Sean Yates, Portal was appointed sporting director at Team Sky, Team Ineos' predecessor, in 2013 and helped Froome to win his first Tour de France title in the same year.
At the time he was the youngest sports director with a World Tour team.
Portal was instrumental in plotting the team's dominance of the Tour de France, helping to steer Froome to a further three Tour de France titles and guiding Geraint Thomas and Egan Bernal to Tour wins in 2018 and 2019 respectively.
"My thoughts are with Nico's wife and children tonight. He was the kindest, happiest guy I knew and always lived life to the fullest. Rest In Peace Nico," Froome said on Twitter.
Former world champion Michal Kwiatkowski said: "I don't want to believe it. Always smiling, always fit, always full of energy. Life is not fair."
Pete Kennaugh, once of Team Sky, said: "My first roommate as a pro. Can't believe the news of Nico Portal passing away. My thoughts and love are with his family who he cherished more than anything. The friendliest, most genuine, kind person you could wish to meet, words can't explain how much he will be missed."
As a rider, Portal's best career result was a stage victory on the Criterium du Dauphine Libere in 2004.
While his nine-year riding career was unspectacular, Portal's deep knowledge of the peloton saw him become one of the most astute Tour tacticians, with Team Sky's riders rarely caught by surprise out on the road.
His pre-Tour dossiers left nothing to chance and his ability to read a race from inside the team car and pass on information earned him respect from across the peloton.
Rival team Deceuninck-Quick-Step said on Twitter: "We are in shock and saddened. Our heartfelt condolences and thoughts go to Team Ineos, the family and friends of Nicolas Portal, a man who loved life and cycling, but was taken too soon."