Born in Panama City to Luis José Varela Arjona and Bexie Esther Rodríguez Pedreschi. Varela is a businessman and entrepreneur, whose family hails from Herrera Province. His paternal grandfather José Varela Blanco emigrated from Bergondo, Galicia in Spain and settled in the district of Pesé, Herrera in Panama. After graduating from Colegio Javier, he attended the Georgia Institute of Technology in the United States, where he graduated with a Bachelor of Science degree in Industrial Engineering in 1985.

He is the son of José Varela and Beixie née Rodríguez. Varela married Panamanian journalist Lorena Castillo in 1992.

Varela entered politics in the early 1990s, becoming chief of the Panameñista Party campaign in 1994 and was the Panameñista Party’s presidential candidate during the 2009 election; Varela joined forces with his rival, Ricardo Martinelli, as vice-presidential candidate, being sworn in on 1 July 2009 as Vice-President of Panama under President Martinelli. Varela won the 2014 presidential election, winning against the ruling-party candidate José Domingo Arias, who was supported by Cambio Democrático, a party led by outgoing President Ricardo Martinelli. Varela won about 39% of the vote against 32% for Arias. The subject announced he would seek to change the legislative body through constitutional changes.