Adam King struck either side of the break in the 2-0 win over Reading at Liberty Stadium.
In March, the Swans' development squad drew with Wolverhampton Wanderers to take the league crown.
The cup final win meant the young Swans celebrated 31 wins across all competitions in 2016-17.
The youngsters' success came after Swansea's senior team survived in the Premier League after Crystal Palace beat Hull 4-0 on Sunday for the latter to be relegated.
Swansea City Under-23s have won their season's double after adding the Premier League Cup to their Premier League Two title.