Mr Barnier, the European Commission’s top Brexit negotiator, promised Brexit would not mean members would need to increase their contributions to the EU’s budget, which topped £136billion last year.
The EU was facing pressure from Germany which feared it would be left to them, the EU’s biggest contributor, to pick up the tab.
Already calculations from Germany’s Federal Court of Auditors estimated Berlin would have to boost its funding by about one third – from €15 billion in 2015 to around €20 billion once the UK leaves.
Fearing the prospect, Gunther Oettinger, the European Budget Commissioner, said the 27 states would have to fill the void that will be left by Britain.
The German politician said in August the EU must stop all rebates and tell all member states to pay more to bankroll common projects.
Mr Oettinger told Germany’s Spiegel magazine: “I could imagine that we try to economise a part and that the remaining 27 member countries agree upon how to contribute the remaining amount.”
The German government’s annual reports highlighted fears that Britain’s departure could have a negative impact on the promotion of structurally weak regions.
It said: “The gross domestic product per capita in the EU will decrease with the departure of Great Britain.
“The EU will be on average purely statistically ‘poorer’, whereas Germany will be purely statistically ‘richer’.
“The positive economic development of the German regions compared to the rest of EU could lead to the fact that in the future the German regions would benefit less from the European Structural Funds.”
Thomas Krüger, a Social Democrat spokesman for the state of Mecklenburg-Western Pomerania (MWP), went to Brussels in September to demand answers, telling reporters Brexit would “rip a hole of around €10billion (£9.2bn) into the EU budget”.
Speaking after Theresa May and European Commission President Jean-Claude Juncker signed off phase one of the Brexit talks, which hinged on the divorce bill, Mr Barnier said: “No member state will have to pay more of receive less because of Brexit, and that is what Theresa May said in her major speech in Florence.
“The UK will honour all the commitments they entered into to during membership.
“The UK will pay neither more or earlier than if it was a member state.
“On this basis we have agreed on the components of the financial settlements and principles and have calculated the value of the payments.”
Despite Britain and the EU agreeing the terms of the settlement, nothing has been decided on the value of the divorce bill.
But Britain will continue to fund projects across the EU, which included £400m to renew a 40 mile stretch of a motorway in Poland this year while the UK’s road networks crumble, and £145,000 to print 736 postcards to “reflect the current problems in Europe that generate social exclusion”.
Mr Barnier said Britain will pay into the 2019/20 budget “as if it were a member state”.
He added: “The UK will participate in programmes from 2014 to 2020 beyond the withdrawal date.
“All commitments entered by the 28 will be honoured by the 28.”