The slogan "No Victor, No Vanquished" was declared by General Yakubu Gowon at the end of the Nigerian Civil War (also known as the Biafran War), which lasted from July 1967 to January 1970.
The war was fought between the federal government of Nigeria and the secessionist Republic of Biafra, led by Colonel Odumegwu Ojukwu. When Biafra surrendered in January 1970, General Gowon, who was the Head of State of the federal government, adopted a policy of reconciliation rather than retribution. His declaration of "No Victor, No Vanquished" was intended to signal that the war's end would not be followed by punishment of the defeated Igbo people, but rather by efforts to reintegrate them into the Nigerian nation.
This policy was part of Gowon's broader programme of Reconciliation, Rehabilitation, and Reconstruction (the "3Rs"). Although the degree to which these promises were fulfilled remains debated, the slogan itself is historically attributed to Gowon as a statement of national unity after the conflict.
Obasanjo played a role in the war as the officer who accepted Biafra's surrender, but the slogan was Gowon's. Ojukwu was the leader of the losing Biafran side. Buhari came to power much later, in a 1983 coup.