Taoiseach backs the 'best man for top EU job'
Close links with Britain not damaged despite UK defeat, says Kenny
Mr Juncker's controversial nomination had been vehemently opposed by British Prime Minister David Cameron.
However, the Tory leader had become increasingly isolated in the run up the key summit.
At the meeting of the 28 EU leaders, Mr Cameron broke with tradition and forced the matter to a vote, but Mr Juncker won out by 26 votes to 2.
The row around Mr Juncker had become very embittered in recent days with direct personalised criticisms of him appearing in British media.
Hungary's Prime Minister Viktor Orban was the only other leader to oppose his candidacy.
Mr Kenny strongly backed Mr Juncker's candidacy despite persistent speculation linking him with the post in recent weeks.
The Taoiseach said he was happy to agree to nominate Mr Juncker, describing him as a highly experienced candidate who knows the inner workings of Europe to an extraordinary extent.
Mr Juncker goes forward now to be ratified by the European Parliament on July 16.
Speaking at the conclusion of the summit, Mr Kenny insisted his relationship with Mr Cameron had not been damaged.
"The relationship has never been stronger with Britain. We continue to work closely with Britain and the prime minister," he said.
Mr Kenny stressed that Mr Cameron made it clear to his fellow leaders that Britain wanted to remain in the EU.
"He has a plan and a strategy that may be so but he said the council must take into account the concerns and the anxieties he has expressed," he added.
Mr Cameron said Mr Juncker's appointment represented a "bad day for Europe".
He said Mr Juncker's election undermines national governments, parliaments, and hands new powers to the European Parliament. Mr Cameron admitted that the "odds were stacked" against him in his attempt to block Mr Juncker, but said he was opposing his nomination on principle.
He added: "There are times when it's very important to stick to your principles (and) your convictions even if odds are heavily stacked against you."
Mr Kenny also spoke of moves by the EU Council to try and stimulate the flagging EU economy in response to last month's European and local elections, which saw a swing against government parties.
The leaders also moved to allow "better use of flexibility" within existing stability and growth pacts.
Ireland along with Greece, France and Spain have been pushing for greater wriggle room. Guardians of fiscal discipline, such as Germany and Finland, have been trying to keep that wriggle room down to a minimum, but German Chancellor Angela Merkel has conceded some ground this week.
EU countries can "make better use of the flexibility already contained in the pacts", summit conclusion documents state.
The leaders also hardened their stance against Russia but have again stopped short of imposing new sanctions.
German Chancellor Angela Merkel has to date been reluctant to escalate tensions with Moscow, but agreed to increase the pressure on Russian Premier, Vladimir Putin.
Ukraine's new president signed a trade and economic pact with the European Union yesterday, pushing his troubled country closer into a European orbit and angering Russia, which warned of unspecified consequences.
A beaming President Petro Poroshenko called it "maybe the most important day for my country" since its independence from the Soviet Union in 1991. The EU Council of the 28 heads of state have set a deadline of next Monday for border checkpoints to be handed back to Ukrainian control and for captured hostages to be released by pro-Russian forces.
If those conditions are not met, then the leaders will assess the situation, and if required, impose further sanctions.