Strains between U.S. military advisers and the Nigerian army over human rights abuses and corruption under Buhari's predecessor Goodluck Jonathan undermined cooperation in efforts to counter the six-year-old Boko Haram insurgency.
The State Department official said Buhari and U.S. Secretary of State John Kerry would discuss future security assistance and expanded economic ties in a meeting on the sidelines of the new president's inauguration on Friday.
The official, speaking on condition of anonymity ahead of Kerry's visit to Abuja, said initial talks with Buhari indicated he wanted a "close relationship" with the United States.
"We have every indication that we'll be able to start a new chapter. We continue to have advisers there ... what I'm talking about would be new advisers in areas where we would expand."
Nigerian security forces have scored some successes against Boko Haram this year. The jihadists held an area of northeast Nigeria roughly the size of Belgium at the start of 2015 but have since been beaten back by counter-attacking government forces backed by those of neighbouring Chad, Niger and Cameroon.
The State Department official said Washington was willing to help train Nigeria's security forces in intelligence and logistics as well as military justice.
"We want to make sure and prioritize based on what President-elect Buhari and his top military team needs," the official said, acknowledging that training of a newly created army battalion last year "ran into some difficulties.
"(But) we think we can pretty quickly get back on track."
Boko Haram launched its insurgency in 2009, attacking towns and villages and killing thousands of people in pursuit of a state adhering to strict sharia law. The militants' abduction of 200 schoolgirls in April 2014 provoked outrage across the world.
The State Department official said that during his discussions with Buhari, Kerry would also express U.S. interest in more economic cooperation with Nigeria, Africa's biggest energy producer and most populous country.
American firms were especially interested in investing in Nigeria's oil and gas sector and in manufacturing.