West Ham will face Fiorentina in their first European final for 47 years after Thursday's 1-0 victory at AZ Alkmaar clinched a 3-1 aggregate success in the Europa Conference League semi-finals.
Pablo Fornals scored West Ham's winner in the final moments of the tense second leg to set up a clash with Fiorentina in the final in Prague on June 7.
The Hammers last reached a major European final in 1976 when they were beaten by Anderlecht in the Cup Winners Cup.
In the other semi-final second leg, Antonin Barak's last-gasp goal sealed Fiorentina's dramatic 3-1 win at FC Basel.
The Serie A club are the first team to reach the final of four different major European competitions.
Vincenzo Italiano's side trailed 2-1 after the semi-final first leg, but they turned the tie around in Switzerland.
Nicolas Gonzalez's double and Barak's goal in the final seconds of stoppage-time in extra-time clinched a 4-3 aggregate triumph.
West Ham have not won a major trophy since Trevor Brooking's goal beat Arsenal in the 1980 FA Cup final.
They lost the 'Steven Gerrard' FA Cup final on penalties after a 3-3 draw against Liverpool in 2006.
"We're absolutely thrilled. It's a big achievement for the club, but now it's about going and winning it. AZ are very good at what they do, but I'm delighted we did it," West Ham boss David Moyes said.
"We've brought in a lot of international players to get better, but we've really struggled this season. We had to go back to what gets you wins, and thankfully we did that."
Last season, West Ham lost 3-1 on aggregate to eventual winners Eintracht Frankfurt in the Europa League semi-finals.
Moyes' side have made amends for that painful near-miss by reaching the final of a competition much-maligned in some quarters, but never again in east London.
West Ham have won 13 of their 14 games in the competition this season and will be favourites whoever they play in the final.
"We have created history. It's the first time in 47 years. It's pure emotion and happiness to get it done," West Ham midfielder Declan Rice said.
Moyes has led West Ham to top 10 finishes in the Premier League in the past two seasons, but they have struggled for much of the current campaign.
They are 15th in the table with two games left, all but mathematically safe from relegation.
Winning a European trophy would be an unexpectedly uplifting end to their troubled season.
West Ham make history
However, their victory over AZ was tarnished slightly after fans from both clubs were involved in fighting after the final whistle.
A group of Alkmaar fans appeared to get into the section holding West Ham's 700 away supporters, prompting ugly scenes before police and stewards quelled the violence.
AZ, sitting fourth in the Dutch Eredivisie, were unbeaten in their last 25 European home matches.
But after a hard-fought clash, West Ham ended that proud record in stoppage-time.
Fornals sprinted clear of the tiring Alkmaar defence to slot a cool finish past Ryan as West Ham were finally able to celebrate a memorable success.
Fiorentina have already appeared in the European Cup, UEFA Cup and Cup Winners' Cup finals.
But the Viola, languishing in eighth place in Serie A, hadn't reached a European final since losing the 1990 UEFA Cup showpiece against Juventus.
Their solitary piece of European silverware came in the Cup Winners Cup in 1961.
Now they have a chance to end that drought.
Gonzalez brought Fiorentina level on aggregate in the 35th minute when he was left unmarked to head in Cristiano Biraghi's corner.
Zeki Amdouni bagged Basel's equaliser in the 55th minute, drilling past Pietro Terracciano after Andy Pelmard's free kick picked out the Swiss forward.
Gonzalez forced extra-time with a clinical finish into the far corner after 72 minutes.
With penalties only seconds away, Barak latched onto Luka Jovic's header and slotted the winner.
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Europa Conference League