From Wikipedia:
The next day (the 31st), in a scene of great confusion, the city of Santa Clara was captured by the combined forces of Che Guevara, Cienfuegos, Revolutionary Directorate(RD) rebels led by Comandantes Rolando Cubela, Juan (”El Mejicano”) Abrahantes , and William Alexander Morgan. News of these defeats caused Batista to panic. He fled Cuba for the Dominican Republic just hours later on January 1, 1959. Comandante William Alexander Morgan, for his part and leading RD rebel forces, continued fighting and captured the city of Cienfuegos on January 1 and 2, during, and in, the wake of Batista’s departure.[9] Castro learned of Batista’s flight in the morning and immediately started negotiations to take over Santiago de Cuba. On January 2nd, the military commander in the city, Colonel Rubido, ordered his soldiers not to fight and Castro’s forces took over the city. The forces of Guevara and Cienfuegos entered Havana at about the same time. They had met no opposition on their journey from Santa Clara to Cuba’s capital. Castro himself arrived in Havana on January 8th after a long victory march, his choice of President, Manuel Urrutia Lleó taking up office on the 3rd
