PARIS—On the night Paris Saint-Germain qualified for the Champions League final and put itself 90 minutes from European glory, the three biggest signings in the club’s history were nowhere near the French capital.

Lionel Messi, Kylian Mbappé, and Neymar, who’d all been signed for this very purpose, were long gone, scattered to Spain, Brazil, and South Florida. The trio of planetary superstars were supposed to be the ones to launch PSG into the stratosphere and bring home a first Champions League trophy.

PARIS—On the night Paris Saint-Germain qualified for the Champions League final and put itself 90 minutes from European glory, the three biggest signings in the club’s history were nowhere near the French capital.

Lionel Messi, Kylian Mbappé, and Neymar, who’d all been signed for this very purpose, were long gone, scattered to Spain, Brazil, and South Florida. The trio of planetary superstars were supposed to be the ones to launch PSG into the stratosphere and bring home a first Champions League trophy.

Instead, they became synonymous with an expensive experiment gone wrong.

Now, after sinking Arsenal 2-1 here on Wednesday and 3-1 overall, PSG is heading to the biggest match in its 55-year existence after one of the most stunning rebuilds in soccer. In the space of two years, the club has gone from creaking vanity project, weighed down by high-priced egos, into the youngest, brightest team to reach the Champions League knockout rounds.

“This has always been one of my objectives: to give our supporters something attractive to watch,” PSG manager Luis Enrique said. “People pay to see a show, and soccer is no different.”

In recent months, Paris has delivered. Despite a lackluster start to its Champions League campaign—at one point, it was facing elimination in the group stage—PSG recovered with a spectacular comeback victory over Manchester City in January. Since then, it has knocked off French rival Brest followed by three English clubs in the past three rounds: Liverpool, Aston Villa, and now Arsenal. Over its past 10 games in Europe, the club has scored 29 goals.

“I’ve defended my team many times throughout the competition,” Luis Enrique said. “We started out playing well, but we were not efficient. When that improved, we showed that we deserved to be in the final.”

The team that Paris will meet on May 31 in Munich, Inter Milan, also knows a thing or two about constructing a roster without superstars—though for decidedly different reasons. The Italian club has spent the past five years digging itself out of a dire financial situation that saw it run up debts of $900 million before being seized by a distressed asset investor last year.

The result is that Inter’s priciest new player of recent seasons was a midfielder signed from the lower reaches of Serie A for a relatively modest (in soccer terms) $35 million. That midfielder, Davide Frattesi, then happened to score the extra-time winner against Barcelona on Tuesday night that sent Inter to the final.

Other budget heroes of this cobbled-together Inter Milan squad include Dutch fullback Denzel Dumfries, who joined for $16 million and scored or assisted five goals across the two legs of the semifinal, and Italy’s Francesco Acerbi, a 37-year-old journeyman who had struggled with testicular cancer, depression, and alcohol in his career, before scoring Inter’s dramatic equalizer against Barça.

“It took a super Inter to give two monstrous performances on the pitch,” Inter coach Simone Inzaghi said after the 4-3 victory. “I’m proud to be their coach, they gave me everything they had.”

Besides reinventing themselves for this run at the title, Paris and Inter do have one other thing in common: Both have fallen at the last hurdle in the past five years. PSG reached its first ever Champions League final in 2020, only to lose 1-0 to Bayern Munich, while the Italian finished as runner-up to Manchester City in 2023.

Of the two, PSG has undergone the more radical transformation. Ever since the club was acquired by an arm of the sovereign-wealth fund of Qatar in 2011, its singular objective has been to win Europe’s shiniest prize. But for 13 consecutive years, it met nothing but frustration as it focused its lavish spending on established stars that routinely crashed out in the round of 16 or quarterfinals.

In fact, the only team in Europe to play more matches than PSG in the Champions League without ever winning it is Arsenal.

It took the exits of Messi, Neymar, and Mbappé for Paris to ask itself hard questions about its identity as a club. The vast Qatari wealth was still there, but the approach needed to change. That’s how PSG found itself shopping a little differently and going into knockout rounds this spring with a squad whose average age was barely over 24.

It invested in youth, speed, and reclamation projects, with the likes of 19-year-old forward Desiré Doué and the previously inconsistent Ousmane Dembélé. And when it needed some flair, it went off the beaten path and signed a Georgian dribbler named Khvicha Kvaratskhelia from Napoli last winter.

It was Kvaratskhelia, who relieved the immense pressure on PSG Wednesday night after goalkeeper Gianluigi Donnarumma held off a 17-minute onslaught by Arsenal. The Georgian broke free on the left and hit the post to rouse the Parc des Princes.

“Stressful,” PSG president Nasser Al Khelaifi said. “Almost heart attack.”

Ten minutes later, the home team had the opening goal of the match. Spanish midfielder Fabian Ruiz, who joined for just $25 million, pounced on a loose ball following a corner, guided it away from a defender with his chest, and fired in the bouncing ball with his left foot.

Defender Achraf Hakimi then added a second for Paris in the 72nd minute that made it easy to forget an earlier missed penalty—and even easier to banish the failures of PSG’s galactico era.

Write to Joshua Robinson at Joshua.Robinson@wsj.com