Varela started his career with Defensor Sporting.[1] He was selected for his professional debut in February 2016 by manager Juan Tejera, who played him for the full duration of a home defeat to Racing Club.[1]Liga MX team Pachuca loaned Varela in 2017, with the defender joining up with the U20 team.[3][4] He made nine appearances for Pachuca's youth team, prior to returning to Defensor Sporting.[4][5] On 1 March 2018, Villa Española of the Uruguayan Segunda División completed the loan signing of Varela.[1] He scored his first senior goal on 2 June against Albion, though he received a straight red card later in the match.[1]
In 2019, Varela joined Fénix.[1] In the following September, Varela departed on loan to European football with Cypriot First Division side Pafos.[6] He didn't appear competitively in 2019–20 due to injury, though was on the substitute's bench for a league match with Apollon Limassol on 14 September.[7] Despite this, the club renewed his loan for a further year ahead of the 2020–21 campaign.[8] He debuted in a goalless draw away to Enosis Neon Paralimni on 23 November.[1]