Rice has been at the centre of Republican criticism over the Obama administration response to a deadly attack on a US consulate in Libya.
Clinton has said she will not serve a second term at the state department.
Any nomination for secretary of state will need to be confirmed in the Senate by a two-thirds vote, enabling Republicans to block her potential appointment.
"I am now convinced that the confirmation process would be lengthy, disruptive and costly - to you and to our most pressing national and international priorities," Rice wrote to the president.
"That trade-off is simply not worth it to our country," she added, saying "The position of Secretary of State should never be politicised."
Obama said in a statement: "I deeply regret the unfair and misleading attacks on Susan Rice in recent weeks."
Rice’s reputation was seriously damaged after her statements in connection with the attack on the U.S. consulate in Benghazi, Lybia, on September 11th . She stated that the tragedy was the result of a spontaneous and initially peaceful protest, not a terrorist attack.
Voice of Russia, Reuters, BBC, RIA