In 2005, at the age of 19, Godín made his debut for Uruguay in a friendly defeat against Mexico in Guadalajara. His first international goal came in another exhibition game, with Serbia and Montenegro in May 2006; he represented the nation at the 2007 Copa América, playing in the opening 0–3 defeat to Peru before losing his place to Andrés Scotti in La Celeste’s run to fourth place.

In August 2007, Godín signed a five-year deal with La Liga side Villarreal CF, scoring in just his second game, a 2–3 away loss against CA Osasuna on 7 October, and participating with 24 matches in their best league placement ever (second). He consolidated his starting position in the subsequent seasons, mostly partnering Argentine Gonzalo Rodríguez in the heart of the back four.

On 4 August 2010, after experiencing his best season at Villarreal – 36 games, three goals – Godín joined fellow league team Atlético Madrid on a five-year contract, after the two clubs agreed an initial fee believed to be around €8 million or £6.6 million. He made his official debut for the Colchoneros on the 27th, playing the entire 2–0 win against Inter Milan for the UEFA Super Cup.

In 2011, Godín featured in Uruguay’s successful 2011 Copa América campaign, making one appearance as a late substitute in a 3–0 defeat of Paraguay in the final after being bedridden for several days with a virus. He also participated in the 2013 FIFA Confederations Cup, partnering Diego Lugano in defence in four of the team’s five matches as they reached the semi-finals.

Godín signed a new contract with Atlético on 1 November 2013, keeping him at the club until 2018. “I’m delighted to prolong my stay with the club. This is my home”, he said. He scored four league goals during the campaign, including one on the last matchday on 17 May 2014 against FC Barcelona which equalised the game at 1–1 to earn his team its first league title in 18 years. A week later, again through a header, he repeated the feat in the final of the UEFA Champions League to put his team ahead, but Real Madrid eventually won 4–1.

In 2015, Godín rejected a transfer to Manchester City, managed by his former Villarreal boss Manuel Pellegrini. On 28 October 2017 he became the foreign player with most appearances for the club, surpassing fellow stopper Luis Perea after his 315th against Villarreal; he was nominated for the 2016 and 2018 Ballon d’Or awards.

In May 2015, Godín was named as captain for Uruguay’s defence of the Copa América during the 2015 continental tournament in Chile. He was also picked for the Copa América Centenario squad, heading home from a Carlos Sánchez long cross in the opener against Mexico where both teams ended with ten players (1–3 loss). He won his 100th cap in the following match, a 0–1 defeat to Venezuela at the Lincoln Financial Field.

On 20 February 2019, Godín scored the second goal in 2–0 home victory over Juventus F.C. in the Champions League round of 16. On 7 May, the 33-year-old announced he would be departing the club after a nine-year tenure and, on 1 June, he symbolically handed over the captain armband to Koke in the 1–1 draw against Sevilla FC.

On 1 July 2019, Inter Milan announced they had signed Godín for free on a three-year deal. It was reported that he had already agreed to a pre-contract the previous January. He made his debut in Serie A on 1 September, coming on for Antonio Candreva for the final 11 minutes of a 2–1 win at Cagliari Calcio.

In June 2019, Godín skippered the team to the quarter-finals of the Copa América in Brazil.

In a season in which Inter finished one point behind champions Juventus, Godín scored his first Nerazzurri goal on 13 July 2020 in a 3–1 home victory over Torino FC. On 21 August he equalised against Sevilla in the 2020 UEFA Europa League Final in Cologne, a 3–2 loss for his side; only five other men had scored in the finals of European football’s two top tournaments.

On 24 September 2020, Godín joined Cagliari on a three-year contract. He played his first match for them on 4 October, in a 5–2 away defeat against Atalanta B.C. where he also scored.