Mr Obama wrote the note in the last moments of his presidency, and it was left for Mr Trump to read once he took office.
Animosity has defined the pair’s relationship for years — for instance, Mr Trump famously offered $US5 million ($6.25 million) to anyone who could produce Mr Obama’s birth certificate, because he claimed Mr Obama was born in Kenya.
Since taking office Mr Trump has hammered his predecessor relentlessly, blaming Mr Obama’s tenure for the challenges he now faces in office.
Mr Obama’s exit memo, which begins respectfully with “Mr. President,” takes a civil tone, but notes of their interpersonal strain shade the missive.
One line hints not so subtly that Mr Trump must repair the wound left by a scarring and divisive campaign battle with Hillary Clinton.
“Millions have placed their hopes in you, and all of us, regardless of party, should hope for expanded prosperity and security during your tenure,” Mr Obama wrote, underlining “all” in the handwritten missive.
Mr Obama was already aware of the Russians’ meddling in the 2016 election when he wrote the letter, which invokes the bad old days of the Cold War.
“American leadership in this world really is indispensable,” Mr Obama wrote. “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.”
Mr Obama even offers Mr Trump a lifeline in the note’s closing.
“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,” the letter concludes.