José Manuel "Conny" Varela Fernández (born February 13, 1954) is a Puerto Rican politician affiliated with the Popular Democratic Party (PPD).

He studied in Notre Dame College of Caguas and graduated from Miguel Meléndez Muñoz High School, where he received a medal for leadership.

Varela completed a bachelor's degree in political science from the University of Puerto Rico, graduating magna cum laude in 1974.

During his last year, he worked at the Puerto Rico Department of Justice, specifically at the Office of the District Attorney.

In 1987, he was selected by the Puerto Rico Department of Sports and Recreation as Distinguished Youth of Caguas, in the category of law.

At the 2008 general elections, Varela was reelected for his fourth consecutive term, and served as minority speaker in the Commissions of Socioeconomic Development, as well as member of the Commissions of Government, Integral Development of the East Region, Public Safety, Housing, and Federal Affairs.