The European Commission president also said it was a "failure and a tragedy" that Brexit is taking place - and said the EU will not be "naive" in its negotiations with the UK once Article 50 is triggered next week.
It has been claimed that Britain could face a Brexit bill of up to £50bn to cover commitments made while it is still a member.
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But it was reported last week that some Cabinet ministers are putting pressure on Philip Hammond to put a £3bn cap on how much the UK is willing to pay.
In an interview with the BBC, Mr Juncker said: "It will be a bill reflecting former commitments by the British government and the British parliament. There will be no sanctions, no punishment, nothing of that kind."
And he added: "We have to calculate scientifically what the British commitments were and then the bill must be paid."
His comments come a day after Michel Barnier, the EU's chief Brexit negotiator, said: "When a country leaves the union, there is no punishment. There is no price to pay to leave, but we must settle the accounts. No more, no less."
Theresa May will formally trigger Article 50 on 29 March, beginning the two-year Brexit process.
Mr Juncker said: "I will be sad, as I was sad when the vote in the referendum took place in Britain - for me, it is a tragedy."
He added: "I am everything but in a hostile mood when it comes to Britain. We'll negotiate in a friendly way, in a firm way and we are not naive."
On the question of EU citizens' rights after Brexit, he said: "I am strongly committed to preserve the rights of Europeans living in Britain and of the British people living on the European continent. This is not about bargaining, this is respecting human dignity."