Security issues are expected to dominate the trip, which comes just months after Islamist militants seized parts of neighbouring Mali.
Her 11-day tour will also take her to South Sudan, Uganda, Kenya, Malawi, South Africa and Ghana.
The US Africa Command, or Africom, has been pumping considerable resources into training forces throughout West Africa.
Mrs Clinton is also expected, in a public address, to hail the country as a democratic example in a region plagued by conflicts and coups.
In March elections, Mr Sall defeated Abdoulaye Wade, who had been in power since 2000 and whose bid for a third term led to deadly protests.
While acknowledging the solid democratic fundamentals that Senegal has built since independence in 1960, the US had repeatedly warned the previous administration about rampant corruption, our correspondent says.
The tour also includes a private meeting with South Africa's anti-apartheid leader Nelson Mandela, now 94, in his hometown of Qunu.