She gave that assessment in a poetic video tribute the State Department released Friday "on behalf of the American people."
Mandela -- an anti-apartheid revolutionary, politician and philanthropist who was South Africa's first black president and first president elected in a fully representative democratic election -- died at age 95 Thursday at his Johannesburg home.
An official memorial service will be held at a World Cup soccer stadium in Soweto Tuesday, President Jacob Zuma said Friday.
Mandela's body will lie in state from Wednesday to Dec. 13. A state funeral will be held Dec. 15 in the small Eastern Cape provincial village of Qunu, where Mandela was born, grew up and retired in May 2012.
Mandela described Qunu, where he will be buried, as the place where he spent his happiest childhood moments.
Angelou -- who is 85 and knew Mandela since the early 1960s, when she was a journalist in Cairo married to South African civil rights activist and lawyer Vusumzi Make -- titled her tribute to Mandela "His Day Is Done."
In her poem, which she recites in the video, Angelou, wearing dark glasses, mourns Mandela's death, which she calls "the slamming of that final door through which no traveler returns."
She says Americans send their souls to South Africans "as you reflect upon your David, armed with a mere stone, facing down the mighty Goliath -- your man of strength, Gideon, emerging triumphant."
"No sun outlasts its sunset, but will rise again and bring the dawn," Angelou says.
"Yes, Mandela's day is done. Yet we, his inheritors, will open the gates wider for reconciliation. And we will respond generously to the cries of blacks and whites, Asians, Hispanics, the poor who live piteously on the floor of our planet," she says.
"Nelson Mandela's day is done. We confess it in tearful voices. Yet we lift our own to say thank you. Thank you, our Gideon. Thank you, our David, our great, courageous man. We will not forget you. We will not dishonor you. We will remember and be glad that you lived among us, that you taught us and that you loved us all."