Two goals from Alejandro Marques set the Blaugrana on their way to victory before Abel Ruiz wrapped up the win with a deflected strike in stoppage time.
Chelsea did go close to getting themselves back into the match, with both Callum Hudson-Odoi and Charlie Brown hitting the woodwork in Nyon.
The Youth League, which runs parallel to the Champions League, was introduced for the 2013-14 season for players under the age of 19.
The tournament is comprised of the 32 teams that qualify for the Champions League at senior level plus 32 more domestic champions.
This is the second time Barcelona been victorious having won the inaugral competition in 2014.
They join Chelsea in having been successful on two occasions, with Red Bull Salzburg the only other winners following their victory over Benfica in the 2017 final.
The win comes as a boost for Barca, whose La Masia academy has come under scrutiny in recent times following a number of high-profile departures.