Teenager De Ligt's 67th-minute header completed a come-from-behind 2-1 win at Allianz Stadium and remarkable 3-2 aggregate triumph in the quarter-finals.
He became the youngest Dutch player to score in a Champions League knockout match since Nordin Wooter in April 1996 for Ajax versus Panathinaikos, and the second youngest defender to every score in a Champions League knockout match behind Joel Matip.
Donny van de Beek had earlier cancelled out Cristiano Ronaldo's header and the visitors were the better side from there, adding the Serie A champions to a list of vanquished heavyweights already including last-16 opponents Real Madrid.
Ajax became the first team from outside the traditional top five European leagues to reach the Champions League semi-final since 2004-05, when fellow Dutch side PSV did so.
"There's still something to play for - we're not satisfied. The next games are also going to be important," captain De Ligt told BT Sport.
"I can't describe what kind of emotion we have. It's unbelievable that a squad from the Netherlands is showing the world what we can do.
"We did it against Bayern Munich, against Real Madrid and now against Juventus.
"We have so much potential, we're all still quite young, and I think everyone saw what we can do.
"We could have scored more, it could have been 4-1, and that's a really big compliment for us."
Ajax have been crowned European champions on four occasions in their proud history, last lifting the trophy in 1995.