The "virtual orchestra" included everything from bell ringers to cellists, all of whom had uploaded their performance to the BBC.
A video combining all 1,200 performances was shown at Proms in the Park events around the UK and as part of BBC Two's coverage of the event.
The Prom also featured an unusual rendition of Rule Britannia.
Peruvian Juan Diego Florez chose to sing the anthem in B Major - the highest pitch ever chosen by a tenor at the event.
"I think it's more comfortable, more exciting, more fun," he told the BBC. "I'm glad that I'm the first one doing it."
The musician stole the show by performing the song in the colourful costume of Manco Capac, governor and founder of the Inca civilization.
Earlier, the dashing tenor had serenaded a cuddly toy of fellow Peruvian Paddington Bear during a performance of Guantanamera - part of a medley of popular Latin songs.
"He is as Peruvian as me," he told the audience. "You know, he was found in Paddington Station... [but] nobody in Peru knows about this.
"Anyway, I know him, I love him."
The build-up to the Last Night was marked by an attempt to hijack the concert's tradition of flag-waving for political means.
Anti-Brexit campaigners handed out EU flags outside the Royal Albert Hall, hoping for a wave of support from Prommers, who more usually wave union flags during the last night.
The organisers, who wanted to remain anonymous, said in a statement: "Music doesn't recognise borders, religion, gender, age, status or creed and most orchestras, shows and music schools rely heavily on talented musicians from inside and outside the EU."
They added: "Accordionist Romano Viazzani summed it up perfectly when he said: 'Music is the universal language. It builds bridges and tears down walls.'"
Prominent Brexit backer Aaron Banks retaliated by pledging to hand out five times as many union jacks as the Brexit team.
In the end, neither side prevailed - as the Royal Albert Hall sported flags from all around the world, including the German, Australian, Danish, Welsh and Cornish flags.
There was also a distinctly international flavour to the programme, conducted by Sakari Oramo, the Finnish music director of the BBC Symphony Orchestra.
He led the musicians through works by French, German, Russian and Italian composers; while Anne Dudley contributed a special arrangement of Fiesta Caribena!
Perhaps in response to the planned protest, Oramo told the audience: "Listening to music in a concentrated way gives us the chanceâ€¦ to find resolution, peace and unity.
"Music enables us to be in dialogue with each other, and our innermost selves. A dialogue which is more necessary in these days than ever before."
The concert also included Michael Torke's Javelin, which was originally performed at the opening ceremony of the 1996 Atlanta Olympics, and a hand-picked selection of young singers performing Vaughan Williams' Serenade to Music - a tribute to Henry Wood, whose name is synonymous with the Proms.
In keeping with tradition, the concert - and the 2016 season - closed with Rule Britannia, Land of Hope and Glory and Jerusalem.
Around the UK, classical music fans were able to join in the celebrations at Proms in the Park events; with special appearances by pianist Ruth McGinley and soprano Lesley Garret in Belfast, Northern Ireland.
Thirteen-year-old Gwydion Rhys was given the opportunity to conduct the BBC National Orchestra of Wales in a performance of Ride of the Valkyries at the Welsh Prom, in Colwyn Bay.
Britain's Got Talent winners Collabro appeared at the Scottish leg, in Glasgow Green; while London's line-up included Frankie Valli and the Four Seasons, Rick Astley, Sir James Galway, Tim Minchin and the cast of Matilda The Musical.
The events brought the two month-long Proms season to a close, after more than 100 concerts.
Highlights included the  SimÃ³n Bolivar Orchestra, from Caracas, who put on a colourful, exotic evening, full of evocations of Latin America; and  a spine-tingling programme of Steve Reich, performed on the roof of a Peckham car park.
A late night Prom paid tribute to the life and music of David Bowie, with mixed results; while Quincy Jones and Strictly Come Dancing were also honoured with their own programmes.
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More than 1,000 amateur musicians have played Bizet's Toreador song, from Carmen, at the Last Night of the Proms.