"I think that the sums that I have seen that they propose to demand from this country seem to me to be extortionate and I think 'to go whistle' is an entirely appropriate expression," Johnson told parliament.
Britain last month began negotiations with the EU to set the terms of its divorce and set a potential timetable for discussing a future free trade deal.
Among the thorny issues to be thrashed out between the UK and the rest of the EU is Britain's estimated 100-billion euro (USD 112 billion) exit bill.
But the true figure could be far lower, as the 100 billion does not account for tens of billions that Britain is set to get back in shared assets and rebates.
Facing questions about Britain's future after Brexit, Johnson also said that "there is no plan for no deal because we are going to get a great deal".
Prime Minister Theresa May - who wants to take Britain out of the EU's single market and customs area in order to limit the free movement of people and strike trade deals with other countries - had previously insisted that "no deal is better than a bad deal".