Abreu set a Cuban home run record in 2010-2011 and was named league MVP. He had played five seasons in the Cuban Serie Nacional through 2007-2008, hitting .295 and slugging .467. After 48 games in 2008-2009, he was batting .345/~.368/.600, earning the infielder a spot on Cuba's provisional roster for the 2009 World Baseball Classic. He did not make the final cut and finished the season with a .346/.441/.630 batting line. He led the 2008-09 Cuban National Series with 30 times hit by pitch. He tied Yenier Bello and Alexander Guerrero for 8th in homers (19), was 8th in slugging and 4th in strikeouts (69).
Abreu was 2 for 10 in the 2009 World Port Tournament, backing up Ariel Borrero at first base. In the 2009 Baseball World Cup, he hit .250/.333/.469 in his first major tournament. He was listed in the IBAF's Final Report as being one of the All-Star outfielders alongside teammate Alfredo Despaigne and Jon Weber, but other sources list Puerto Rico's Miguel Abreu, who had better statistics. He was not even used as a starter in the outfield, playing alongside Ariel Borrero at first. In the Gold Medal game, he did not appear as Borrero saw the action.
In 2009-2010, Abreu had his best year yet, hitting .399/.555/.822 with 82 runs, 30 homers, 76 RBI and 74 walks to 49 strikeouts in 89 games. He tied Leonys Martin for 6th in the Serie Nacional in runs, tied for third with 25 doubles, tied Yulieski Gourriel for second in home runs (one behind Alfredo Despaigne in a to-the-wire home run race), was third with 235 total bases (behind Despaigne and Gourriel), again led with 30 times hit by pitch, tied Enrique Esteban Diaz for 4th in walks, led with 32 intentional walks (12 more than runner-up Yosvany Peraza), was second in average (.005 behind Despaigne), led in slugging (.008 over Despaigne) and probably led in OBP. He was named the All-Star first baseman.
Abreu was Cuba's starting first baseman when they won the 2010 Intercontinental Cup, their first Gold in an international tournament in three years. He hit .292/.320/.500. In the finale, he went 1 for 3 and scored the first run in the victory over the Dutch national baseball team; he doubled off Rob Cordemans in the third and came home on a Yorbis Borroto hit. He helped Cuba finish second at the 2010 Pan American Games Qualifying Tournament. In the 2010 World University Baseball Championship, he posted the best average by going 10 for 18 with 2 walks, a double, triple, four homers, 9 runs and 12 RBI in six games as Cuba won the Gold. He was 0 for 4 in the finale, as Cuba edged Team USA. He was named the event's All-Star 1B.
Abreu continued to improve in 2010-11 Cuban National Series with one of the greatest seasons in Cuban history. He hit .453/.597/.986 with 79 runs, 93 RBI and 33 home runs in only 66 games. Despite missing 23 games due to bursitis in his shoulder, he broke Despaigne's home run record (as did Yoenis Cespedes - both hit their 33rd on the season's last day). Despaigne would reclaim the record a year later. Abreu led the league in average (.052 over Michel Enriquez), slugging (a whopping .212 over runner-up Frederich Cepeda), intentional walks (21) and homers (tied with Yoenis Cespedes), was second in RBI (6 behind Cespedes), tied for 8th in runs with Donal Duarte, was 7th in total bases (209) and 4th in times hit by pitch (21). Had he not been injured, he would have likely easily won a Triple Crown. He won Cuban National Series Most Valuable Player Award. He was the second MVP from Cienfuegos, following Pedro Jose Rodriguez, Sr. by 31 years.
Abreu was named to the Cuban national baseball team for the 2013 World Baseball Classic. In Cuba's six games, he batted .383 and hit three home runs while recording nine RBIs. In August 2013, Abreu defected from Cuba, to test the MLB free agent market. His defection was later confirmed by former teammate Henry Urrutia. He established residency in the Dominican Republic, and was named a free agent. In October, he signed a six-year contract with the Chicago White Sox worth $68 million