The drought will end for one of the clubs when they play out the Europa Conference League final on Wednesday in Prague.
Thousands of fans from both sides have descended on the Czech capital. Only 6,000 tickets were reserved for supporters of the Hammers and La Viola, the rest of Eden Arena's 19,000-person capacity will be used by UEFA for its needs.
Two separate fan zones have been reserved for travellers without a ticket.
West Ham earned its lone European title in 1965, the old European Cup Winners’ Cup. Alan Sealey scored twice to beat 1860 Munich 2-0 at Wembley Stadium. The Hammers reached the final again in 1976.
Fiorentina's only European trophy was also the UEFA Cup Winners’ Cup, the first in 1961 when it defeated Rangers in a two-leg final 4-1 on aggregate.
By reaching the second final of the Europa Conference League, Fiorentina has become the first club to contest a final in four major continental competitions.
Real Madrid defeated Fiorentina in the 1957 European Cup (the forerunner of the Champions League) and was overcome by Juventus in the 1990 UEFA Cup final. It also failed to win the UEFA Cup Winners' Cup back-to-back, losing the 1962 final to Atletico Madrid.
Fiorentina has had a good buildup. It played the Italian Cup final two weeks ago and was beaten by Inter Milan 2-1. That's the only loss for the Florence-based club in its last six matches. The last warmup for the Conference final was beating Sassuolo 3-1 last Friday for an eighth-place finish in Serie A.
“We needed this victory,” Fiorentina coach Vincenzo Italiano said after the match. “Now we have a mountain to climb but we will be aiming for the summit in Prague.”
Despite struggling to a 14th-place finish in the English Premier League, West Ham has been a European title contender for a second straight year under manager David Moyes.
Following a campaign to the Europa League semifinals a year ago, West Ham marched to Prague as the only undefeated team in the third-tier Europa Conference League.
West Ham won 13 games including the qualifiers and was held by Gent to 1-1 in the first leg of their quarterfinal. The Hammers were the first club to win all six group-stage encounters.
“They’re a team that has a lot of ability, they’ve got some top-level players, they have got strength all over the pitch,” Italiano said about West Ham in Prague on Tuesday. “But if we’ve made it to the final, then we clearly have some strength as well."
In the Czech capital, West Ham will face a team that scored the most goals in the campaign, 36, led by forward Arthur Cabral's seven.
The reward for the winner of the final is not just a trophy but also a berth in the Europa League next season.