Jean-Claude Juncker gave one last news briefing before he hands over power to Ursula von der Leyen.
The Commission handover was delayed a month after parliament rejected three commissioner-candidates from Hungary, Romania, and France.
The former German defence minister’s new Commission was approved by the European Parliament on Wednesday.
Charles Michel, the former Belgian prime minister, took over the EU Council from Donald Tusk earlier in the day.
The outgoing European Commission president joked about the Prime Minister’s interest in “the curvature of cucumbers” in his previous career as a Brussels-based journalist.
He also made sport of the time taken for Britain to “enfin!” find the exit door from the EU since the 2016 referendum, adding: “Four years later, I will be leaving before the UK does.”
“Over these past years, I often felt like Europe’s family therapist, trying to keep everyone happy and on board,” Mr Juncker wrote in a farewell letter for the Politico news service.
On Brexit, he proudly pointed to the strength of the EU side in negotiations. “When it came to Brexit I hired the most capable divorce lawyer in town, mon cher Michel [Barnier], who (twice) negotiated the best divorce deal possible while making sure the EU27 family sticks together,” he said.
Bidding farewell to the still unended Brexit saga, Mr Juncker said: “In a way, I am not unhappy about this because it breaks my heart to see a member of our Union leave its midst