The so-called big six Premier League clubs have won their persistent battle to be paid a greater share of the income from its burgeoning international TV rights which have for 26 years been shared equally between all the league’s clubs.

Led by Manchester City and Liverpool, supported by Manchester United, Arsenal, Chelsea and Spurs, the six have pressed the case that as they are the prime attractions for global audiences and money paid by international broadcasters, they should receive more of the money.

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This is a landmark change to a key element of the rules and which has helped to preserve a measure of financial and on-field competitiveness ever since the First Division clubs broke away from the Football League’s inter-divisional sharing arrangements and formed the Premier League in 1992.

As 14 clubs must approve any change to the Premier League’s rules, the required majority had not been obtained until the summer club meeting on Thursday when the executive chairman, Richard Scudamore, announced the change. Under constant pressure from the six, with Liverpool’s majority owner John Henry having pressed the case publicly recently, Scudamore came up with a compromise which secured the majority.

From 2019-20, the first season of TV deals being concluded now, the current level of revenue from international TV rights sales, £3.3bn, will still be shared equally between all 20 clubs. Any increase on that level, which Scudamore is understood to be confident of securing, will then be distributed according to where a team finish in the league. So the six, confident of finishing in the higher places every season for the foreseeable future, will for the first time be paid more of the international TV rights revenues on that basis.

The UK TV rights money, currently £5.1bn, has always been shared out equally, part according to where a team finish, and part according to how many times they are shown on TV, which also favours the more successful clubs.

Part of the compromise reached is that the difference this makes to the earnings of the top six will be capped. The Premier League pointed out that currently the highest-earning club from TV and sponsorship central distributions, the title-winning Manchester City, were paid £149m, approximately 1.6 times more than the lowest-earning, bottom-finishing West Brom, who made £95m.

The differential now the international money-sharing formula is to be changed will be 1.8, Scudamore said, and any income above that will be shared to maintain that differential. Proponents of the rule change, including the clubs which pushed for it, argue that the entirely equal sharing had become outdated as the rule was established in 1992, when the international rights were negligible.

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Scudamore, hailing the change as an unalloyed positive, said in a statement: “This … further incentivises on-pitch achievement and maintains the Premier League’s position as the most equitable in Europe in terms of sharing central revenues. By coming together and agreeing this change, the clubs have provided a platform for the future success of the League for many years ahead.”

However, opponents argue that the richer clubs are already inhabiting a different financial plane, and should not be enabled to stretch even further away. It is also seen by some as a dangerous step to change a foundational rule, allowing the new formula, and the cap, to be challenged again in the future.

The Premier League also announced that its two smaller remaining UK and Ireland live broadcasting deals had been sold, to BT Sport and, for the first time, to the internet platform Amazon Prime Video.

The change has been agreed at a time of more generally advancing financial ambitions of the major European clubs. Andrea Agnelli, the chairman of Juventus and the European Club Association, told the Guardian in a recent interview that he wanted to “reshape” European football by having more lucrative matches played in the Champions League from 2024. The Fifa president, Gianni Infantino, also recently proposed a new 24-team format for the Club World Cup which would deliver $3bn for each four-yearly tournament. That proposal has been shelved.