- They have not been without silverware in the past 30 years, winning three FA Cups, four League Cups, a Uefa Cup, the Champions League twice - the latest coming last season under Klopp - as well as three Super Cups and one Club World Cup.
Liverpool's 30-year wait for a top-flight title is over after Manchester City lost 2-1 at Chelsea to confirm the Reds as Premier League champions.
Jurgen Klopp's side needed one victory to seal the league but City's failure to win means they cannot be caught.
It is Liverpool's 19th top-flight title and their first since 1989-90.
Despite being urged to "stay home" by the city's metro mayor because of coronavirus, thousands of fans gathered at Anfield to celebrate.
Chelsea 2-1 Manchester City | PREMIER LEAGUE HIGHLIGHTS | 6/25/2020 | NBC Sports
Many of the supporters who congregated at the club's ground wore face masks and some lit flares.
A number of Reds players, including goalkeeper Alisson, defender Virgil van Dijk and midfielder Alex Oxlade-Chamberlain, celebrated together after watching the Chelsea-City game.
Klopp, wearing a Liverpool shirt and clearly emotional, told Sky Sports: "I have no words, it's unbelievable.
"It's much more than I ever thought would be possible. Becoming champion with this club is absolutely incredible.
"I haven't waited 30 years - I have been here for four and a half years - but it is quite an achievement, especially with the three-month break because nobody knew if we could go on.
"I know it is difficult for people in this moment but we could not hold back. We will enjoy this with our supporters when we can."
As the global pandemic disrupted life in England and led to the suspension of the Premier League for three months, Liverpool supporters endured a nervous wait to see how the season would end, with some early suggestions it might have been declared null and void, thus wiping their remarkable efforts from the record books.
The Premier League's return this month enabled them to cap their stunning success.
However, because of the measures put in place in response to the virus, Liverpool will not be able to celebrate their long-awaited success with their supporters immediately, at least not in the traditional sense.
As with Wednesday's impressive 4-0 win over Crystal Palace, when they next play at Anfield - against Aston Villa on Sunday 5 July, and for their two other remaining home games - it will be behind closed doors.
It also seems unlikely they will be able to take part in any of the usual public events in Liverpool, such as an open-top bus parade around the city.
By a quirk of fate, though, the next time they take to the field will be at the side they have beaten to this season's title and who pipped them so narrowly last campaign, Manchester City.
Following their defeat at Chelsea, City boss Pep Guardiola congratulated Liverpool on their title success.
A record-breaking season
Winning the title was always the main aim for a club which endured such a long wait to be crowned champions of England again, having earned that honour 11 times between 1973 and 1990.
Things could get better yet, with City's 100-point total for a season one of numerous records Liverpool can still break.
Klopp's side have produced one of the most memorable campaigns in Premier League history, amassing 86 points with 28 victories, two draws and a single defeat from 31 games.
Also still a possibility are the most wins in a season (the record is 32), most home wins (18), most away wins (16) and biggest winning margin (19 points).
Their title win this season is the earliest on record, at least with regard to games remaining, with the Reds having seven to play.
That it is not the earliest title win by date is only because of the halting of football in England between March and May as a result of the coronavirus pandemic.
Thirty years of hurt...
Liverpool's triumph represents a huge moment for their fans, who grew accustomed to success in the 1970s and 1980s, including a run between the 1972-73 and 1990-91 seasons in which they failed to finish first or second in the league only once.
They have not been without silverware in the past 30 years, winning three FA Cups, four League Cups, a Uefa Cup, the Champions League twice - the latest coming last season under Klopp - as well as three Super Cups and one Club World Cup.
However, since Kenny Dalglish led them to the First Division championship, they have had to endure three decades without league success, during which their record tally of titles was surpassed by rivals Manchester United, who have 20 to their name.
It was during this period that United boss Sir Alex Ferguson famously revelled in having "knocked Liverpool off their perch".
Liverpool have come close during that time to restoring themselves to the top of the English game, finishing second in the Premier League four times.
Gerard Houllier (2001-02) and Rafael Benitez (2008-09) both took them close.
Famously, in the 2013-14 season, Brendan Rodgers' side looked as though they were going to take the crown but a late-season slump - synonymous with a Steven Gerrard slip that enabled Chelsea to score and win at Anfield - saw them fall agonisingly short.
Last season, they racked up a stunning 97 points, losing only one game all campaign, but had the misfortune of coming up against an even better Manchester City side, who beat them to the title by a point. No side had ever earned so many points without winning the league.
Klopp takes Reds from 10th to title
The appointment of Klopp has been pivotal to Liverpool's rise in recent seasons to this moment of success.
The German arrived at Anfield in October 2015 following the sacking of Rodgers and with the club 10th in the Premier League.
Klopp arrived with a record of success, having led Borussia Dortmund to two Bundesliga titles and the 2013 Champions League final, and with a reputation for fast-paced, high-pressing attacking play, which he described as "heavy metal football".
His four full seasons to date have yielded finishing positions of fourth, fourth, second and now first.
Intelligent dealing in the transfer market has also been key to his success, with Mohamed Salah and Sadio Mane signed during his reign. Along with Roberto Firmino, who arrived shortly before Klopp, the trio have scored a sensational 211 goals in less than three seasons (92 for Salah, 65 for Mane and 54 for Firmino).
The additions of world-class goalkeeper Alisson and centre-back Virgil van Dijk were also crucial.
Klopp has also improved players who were at the club before he arrived, including midfielder Jordan Henderson - his captain - and young full-back Trent Alexander-Arnold.
Klopp is the only Liverpool manager since Dalglish left (including the Scot himself during a second spell from January 2011 to May 2012) with a win percentage over 60.
Dalglish delivered Liverpool their 16th, 17th and 18th league titles and now, after 30 years, they have found a fitting successor to provide them with their 19th.
"The last two years and since Jurgen's come in has been very positive," Dalglish told BT Sport. "He's been fantastic and epitomises everything Liverpool football club stands for. Whatever they got, they have deserved it.
"Onwards and upwards. We have a lot more happy days to look forward to as long as Jurgen is here."
Such has been their dominance, at one stage they led the table by 25 points - a record gap between a side in first and second in the English top flight.