The tradition involves a handwritten note, which the outgoing president leaves in the center drawer of his desk in the Oval Office for his successor. Let’s see if Mr Trump will continue the tradition and leave a letter for the new Mr. President Joe Biden.
By the way, the tradition began with Ronald Reagan, who scribbled a note on stationary paper, leaving it for George H. W. Bush to find when he sat down. That single act left an impression on Bush, so much so that he followed suit. Despite suffering a difficult loss to Bill Clinton in 1993, Bush still wrote him a letter.
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Final Message from President Barack Obama to all Americans, 2017: Barack Obama alluded to in his thank you message to the nation on Thursday, the eve of his stepping down as president:
“My fellow Americans,
It’s a long-standing tradition for the sitting president of the United States to leave a parting letter in the Oval Office for the American elected to take his or her place. It’s a letter meant to share what we know, what we’ve learned, and what small wisdom may help our successor bear the great responsibility that comes with the highest office in our land, and the leadership of the free world. But before I leave my note for our 45th president, I wanted to say one final thank you for the honor of serving as your 44th. Because all that I’ve learned in my time in office, I’ve learned from you. You made me a better President, and you made me a better man. Throughout these eight years, you have been the source of goodness, resilience, and hope from which I’ve pulled strength. I’ve seen neighbors and communities take care of each other during the worst economic crisis of our lifetimes. I have mourned with grieving families searching for answers — and found grace in a Charleston church. I’ve taken heart from the hope of young graduates and our newest military officers. I’ve seen our scientists help a paralyzed man regain his sense of touch, and wounded warriors once given up for dead walk again. I’ve seen Americans whose lives have been saved because they finally have access to medical care, and families whose lives have been changed because their marriages are recognized as equal to our own. I’ve seen the youngest of children remind us through their actions and through their generosity of our obligations to care for refugees, or work for peace, and, above all, to look out for each other. I’ve seen you, the American people, in all your decency, determination, good humor, and kindness. And in your daily acts of citizenship, I’ve seen our future unfolding. All of us, regardless of party, should throw ourselves into that work — the joyous work of citizenship. Not just when there’s an election, not just when our own narrow interest is at stake, but over the full span of a lifetime. I’ll be right there with you every step of the way. And when the arc of progress seems slow, remember: America is not the project of any one person. The single most powerful word in our democracy is the word ‘We.’ ‘We the People.’ ‘We shall overcome.’ Yes, we can.”
From President Barack Obama to President Trump, 2017:
“Dear Mr. President – Congratulations on a remarkable run. Millions have placed their hopes in you, and all of us, regardless of party, should hope for expanded prosperity and security during your tenure. This is a unique office, without a clear blueprint for success, so I don’t know that any advice from me will be particularly helpful. Still, let me offer a few reflections from the past 8 years. First, we’ve both been blessed, in different ways, with great good fortune. Not everyone is so lucky. It’s up to us to do everything we can (to) build more ladders of success for every child and family that’s willing to work hard. Second, American leadership in this world really is indispensable. It’s up to us, through action and example, to sustain the international order that’s expanded steadily since the end of the Cold War, and upon which our own wealth and safety depend. Third, we are just temporary occupants of this office. That makes us guardians of those democratic institutions and traditions — like rule of law, separation of powers, equal protection and civil liberties — that our forebears fought and bled for. Regardless of the push and pull of daily politics, it’s up to us to leave those instruments of our democracy at least as strong as we found them. And finally, take time, in the rush of events and responsibilities, for friends and family. They’ll get you through the inevitable rough patches. Michelle and I wish you and Melania the very best as you embark on this great adventure, and know that we stand ready to help in any ways which we can. Good luck and Godspeed, BO”
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From President George W. Bush to President Barack Obama, 2009:

Jan. 20, 2009
“Dear Barack,
Congratulations on becoming our President. You have just begun a fantastic chapter in your life. Very few have had the honor of knowing the responsibility you now feel. Very few know the excitement of the moment and the challenges you will face. There will be trying moments. The critics will rage. Your “friends” will disappoint you. But, you will have an Almighty God to comfort you, a family who loves you, and a country that is pulling for you, including me. No matter what comes, you will be inspired by the character and compassion of the people you now lead. God bless you. Sincerely, GW”
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From President Bill Clinton to President George W. Bush, 2001:

January 20, 2001
“Dear George,
Today you embark on the greatest venture, with the greatest honor, that can come to an American citizen. Like me, you are especially fortunate to lead our country in a time of profound and largely positive change, when old questions, not just about the role of government, but about the very nature of our nation, must be answered anew. You lead a proud, decent, good people. And from this day you are President of all of us. I salute you and wish you success and much happiness. The burdens you now shoulder are great but often exaggerated. The sheer joy of doing what you believe is right is inexpressible. My prayers are with you and your family. Godspeed. Sincerely, Bill”
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From the First President George W. Bush to President Bill Clinton, 1993:

Jan. 20, 1993
“Dear Bill,
When I walked into this office just now I felt the same sense of wonder and respect that I felt four years ago. I know you will feel that, too. I wish you great happiness here. I never felt the loneliness some Presidents have described. There will be very tough times, made even more difficult by criticism you may not think is fair. I’m not a very good one to give advice; but just don’t let the critics discourage you or push you off course. You will be our President when you read this note. I wish you well. I wish your family well. Your success now is our country’s success. I am rooting hard for you. Good Luck — George”