Following the 2011 season, Verdugo was traded by the Giants to the Kansas City Royals with Jonathan Sánchez for Melky Cabrera.

Verdugo was designated for assignment by the Royals on November 20, 2012 as they cleared room on the 40-man roster ahead of the Rule 5 draft.

[6] On November 20, 2014, Verdugo, along with LHP Jim Fuller, signed a minor league contract with the Oakland Athletics organization.

On April 28, 2016, Verdugo signed with the Rojos del Águila de Veracruz of the Mexican Baseball League.

On February 14, 2018, Verdugo signed with the Uni-President Lions of the Chinese Professional Baseball League.

[8] On October 7 of the same year, Verdugo completed the first (and, to date, only) perfect game in CPBL history.

On October 13, 2021, Verdugo, along with IF Jose Vargas and P Andrew Morales, were traded to the Saraperos de Saltillo of the Mexican League in exchange for OF Juan Perez.

On February 24, 2023, Verdugo's rights were re-acquired by El Águila de Veracruz of the Mexican League.