He never lost at a major event (world championships, Olympics) and beat fellow Cuban Félix Savón in two of their three fights.

In 2001 he beat Russian Olympic silver medalist of 2000 Sultan Ibragimov in the semifinals on points and in the final British David Haye by TKO.

He defected from the national Cuban boxing team in December 2006, during training in Venezuela for the Pan-American Games in Rio de Janeiro.

With him, came two fellow amateurs and reigning Olympic champions, Yan Barthelemí Varela and Yuriorkis Gamboa Toledano.

In the next 18 months he racked up an 11–0 record against creditable opposition at this stage of a professional career, and in October 2008 he defeated Chauncy Welliver for the WBC international heavyweight title.

Solis fighting out of Miami, Florida, made his third successful defense of the WBC International Heavyweight title with a second round stoppage of Monte Barrett of Queens, New York.

[2][3] On 11 January, it was official confirmed that the fight between Vitali Klitschko and Solís was going to take place in Cologne, Germany, on 19 March 2011.

In the first round of the fight, after the ten-second warning bell rang, Solis threw a left and right which didn't connect, to Klitschko's chin.

The slow motion shows that he was momentarily stunned by the almost grazing temple punch, and his foot froze to the canvas, whilst his leg and body continued backwards, causing an injury to his ankle.

Solis launched a comeback following his rehabilitation from knee surgery and scored three consecutive victories over the next three years including points wins over Konstantin Airich and undefeated prospect Leif Larsen.

The first was by a close split decision and the second by TKO as Solis retired in his corner for reasons unknown midway through the bout.