The pair were photographed chatting together while enjoying tea on Thursday and, according to the Washington Post, steered away from Donald Trump's controversial success against Hillary Clinton. Instead, the pair spoke about raising children before taking a tour of the private residence of the White House, including the Truman Balcony and the State Floor.
Michelle and Melania met for tea
Donald tweeted about the pair meeting later that day, writing: "A fantastic day in D.C. Met with President Obama for first time. Really good meeting, great chemistry. Melania liked Mrs. O a lot!"
Anita McBride, who originally served George W. Bush's wife Laura, speculated about the issues Melania will be focussed on as First Lady, telling CBS: "I think she's given us a little bit of a hint of what she thinks she would like to work on and that is the issue of social media with young children.
"It's a position description that gets rewritten with each person and we will adapt to it, the White House will adapt to its new occupant, and the occupants will adapt to the White House and so will Americans."
White House spokesman Josh Ernest has also opened up about how the former model will handle the move to the White House.
Donald and Barack shook hands at the White House
"Mrs Obama has talked before publicly about the stresses and anxieties of moving to a new place, living inside a fishbowl, moving inside a museum and raising her family there," he said.
"And I'm sure that Mrs Trump is feeling many of those same anxieties."
Barack Obama spoke about his meeting with the President-elect, saying: "It was wide-ranging. We talked about some of the organisational issues in setting up a White House.
"I have been very encouraged by the interest in President-elect Trump's wanting to work with my team around many of the issues that this great country faces and I believe that it is important for all of us regardless of party and regardless of political preferences to now come together, to work together to deal with the many challenges that we face."