In a televised New Year message, Paul Kagame said he would seek to extend his presidency by seven years, from 2017. The widely expected confirmation follows a successful referendum last month on constitutional changes.
Kagame told Rwandans on Friday that he didn't think the country needed "an external leader" at this point in its history.
He spoke of the importance of "maintaining political stability" to help build the nation's "prosperity."
While stating categorically that he didn't want to be President for life, Kagame told viewers on national TV: "You requested me to lead the country again after 2017. Given the importance and consideration you attach to this, I can only accept."
"You clearly expressed your choices for the future of our country. The process allowed us the time to make certain that the proposed changes had merit and wisdom," he added, in his TV address.
Kagame was formally elected in 2000 but has run Rwanda since his ethnic Tutsi rebel army ended the 1994 Rwandan genocide by extremists from the Hutu majority.
18 more years?
He was initially limited to two terms in office. But the constitutional changes mean that he could now remain in power until 2034 if he wins future elections. He could run for a seven year term in 2017 followed by two consecutive five year terms.
While most observers accept that he has broad support to continue rebuilding the nation following the massacre of an estimated 800,000 people, he is also accused of stifling the media and opposition voices, which he has denied.
Rwanda's sole opposition party, the Democratic Greens, has no seats in parliament and had its bid to block changes to the constitution rejected by the courts.