The extension, made possible by a recent legislative change allowing Italian clubs to offer contracts of up to eight years rather than the previous five-year maximum, comes with a significant pay rise for the 21-year-old striker, whose net salary is set to almost triple from around €1.2m to €2.7m per season.
Esposito made a strong impression in his first season as a regular in Inter Milan's first team, contributing to the club's domestic double under Cristian Chivu and earning his first Italy caps along the way.
Speaking to Inter's official channels after signing, Esposito described the moment as one of the most significant of his career so far.
"For me this is something exciting — when I got in the car to come here I had butterflies in my stomach. It's an important milestone for my life and my career, but not a final destination," he said.
"It's simply recognition for the work done up to now, and motivation to keep working this way."
Asked what he would say to the nine-year-old boy who joined Inter's youth academy back in 2014, Esposito reflected on the journey that has brought him to this point.
"I'd tell him to always believe in it, in the good moments and the less good ones. To always believe and work as hard as possible," he said.
The striker also spoke about the influence of head coach Chivu, who first worked with him at Under-14 level before their paths crossed again in Inter's first team.
"He's been very important, I even did my Under-14s with him. He's always had faith and trust in me, and finding him again in the first team was important — he gave me the chance I'd dreamed of my whole life, and I'm happy to have repaid that trust so far, and I hope to keep doing so in the future," Esposito said.
Looking ahead, the young forward was reluctant to set specific targets but made clear his ambitions remained high.
"In terms of trophies and statistics, I don't want to settle — I don't like giving numbers, but I want to keep improving as a player and as a person," he said, before thanking Inter's supporters for their backing.
"I'm grateful to them — from the day I returned to the first team, I've been welcomed incredibly. I thank them and I'm happy to continue this adventure together."