Tagliafico arrived from Argentina's Club Atlético Independiente in early January, 2018. He made his debut appearance on 21 January that year, in the home fixture against Feyenoord (2-0). In his first season playing for Ajax, Tagliafico eventually appeared fifteen times, scoring once; at home against sc Heerenveen on 11 March 2018 (4-1).
The 2018/2019 season became turned out to be Tagliafico's most successful. The left-back was, for instance, part of the successful UEFA Champions League squad and was instrumental in their amazing journey through Europe. The Argentinian was a force to be reckoned with, thanks to his strength and attack mindset, and scored three goals in the UEFA Champions League; two in the home game against AEK Athens and another also on home turf in the spectacular game against FC Bayern Munich.
Tagliafico was also of great value to the Amsterdam side at the domestic level. During the semi-finals of the Dutch cup, away to Feyenoord (3-0), the Argentinian scored the all-important second goal for Ajax just after half time. Tagliafico eventually won the double that season with Ajax, scoring twice in the Eredivisie — at home against ADO (5-1) as well as away to De Graafschap in the cup game (4-1).
Next season, Tagliafico scored again in the UEFA Champions League. This time in the preliminary round against PAOK Thessaloniki (3-2), as well as in the group stages against the French side, Lille. He put the ball into the net twice in that competition. In the meantime, the popular Argentinian has become a public favourite in Amsterdam thanks to his playing style, fighting spirit and dedication, and in April 2020 he extended the contract binding him to Ajax until the summer of 2023.
In his penultimate season, Tagliafico won the double for the second time with Ajax. He scored just once that season, away to PEC Zwolle (2-0). The Argentinian also played throughout the European championship, where Ajax eventually lost on aggregate against AS Roma in the quarter-finals of the Europa League.
In 2022, Tagliafico became a champion with Ajax for the third time in his career. He scored playing away to Fortuna Sittard and notched up his final goal for Ajax in the championship game at home against sc Heerenveen.
Ahead of the home fixture with RKC Waalwijk on 6 March, 2022, the defender was very much in the spotlight because it would be his 150th official match for the Ajax first team. Tagliafico eventually made 169 official appearances for the Ajax main squad and scored sixteen goals. The Argentine international was a national champion three times with Ajax (2019, 2021 and 2022) and held the Dutch cup aloft twice - in 2019 and in 2021. He even won the Johan Cruijff Shield in 2019.