In an embarrassing intervention for the Prime Minister, who last week failed in his bid to stop the Luxemburger getting the job, Mr Clarke said: "I am one of a handful of British politicians who knows Jean-Claude Juncker and has known him for many years.
"I am perfectly happy that he's president of the European Commission and, more to the point, my prime minister has rung him up and agreed to work with him."
The former Chancellor was speaking at a conference of business supporters of German Chancellor Angela Merkel, who pushed through Mr Juncker's candidacy.
Mr Cameron pursued a very public campaign to block Juncker's candidacy, making clear that he saw him as a veteran advocate of closer EU integration who was ill-suited to pursuing the reforms favoured by Britain and voters in other countries where Eurosceptic parties did well in May's European elections.
But Britain and Hungary were the only two of the EU's 28 members to oppose Mr Juncker at last week's EU summit, leaving Mr Cameron facing opposition accusations of having failed to build alliances and of squandering Britain's influence in Europe.