Kenyans in Mr Obama's ancestral homeland stayed up all night and danced with joy as America's first black president won a second term in the White House.
Hundreds gathered in his late father's village, and cheers and chants of "Obama, Obama, Obama!" erupted.
The President's grandmother, Sarah, told reporters: "He is welcomed home. I would just like to tell him to give his best to the people who have shown their faith in him by electing him."
Russian President Vladimir Putin said he hoped Mr Obama's re-election would have a positive impact on relations with the US.
Despite the President's call for a reset in ties with Russia, relations have been strained. Mr Putin's spokesman said: "Overall the Kremlin welcomes the news of Barack Obama's victory in the elections.
"We express hope that the positive beginnings in bilateral relations and in international co-operation between Russian and the US, in the interest of international security, will develop and improve."
Germany's Chancellor Angela Merkel said she hoped for a continuation of their work which has been conducted "in a spirit of friendship".
The Vatican congratulated Mr Obama on his re-election but highlighted the thorny differences between the Catholic Church and his administration over abortion and healthcare.
Israeli Prime Minister Benjamin Netanyahu, who has had a strained relationship with Mr Obama over Iran and the Israeli-Palestinian conflict, said the result would not make any difference.