The Colts later announced the extension but did not disclose terms.
"We want to take care of our players," general manager Chris Ballard said earlier this week.
Smith, a second-round pick in 2018, spent the majority of his college career at Auburn playing guard. But the Colts developed him into a right tackle after selecting him, and he became the full-time starter at the position early in his rookie season. He's helped the Colts have one of the top offensive lines in the NFL, playing alongside center Ryan Kelly and guards Mark Glowinski and Quenton Nelson.
"It's a little bit of relief, knowing where you're going to be at the next couple of years," said Smith, who asked his agent to get a deal done before the start of the regular season. "I love this organization. Thank [owner] Mr. [Jim] Irsay, Chris Ballard in believing in me. I feel like Indianapolis is my home. They paid me, so I want to pay them back. Want to play my best football, help them win as many games as we can."
Signing Smith is the start of what should be several contracts the Colts give out to what turned out to be an impressive 2018 draft class.
Darius Leonard, who has become one of the top linebackers in the NFL, is also in line to get an extension. He has 416 tackles, 15 sacks, seven interceptions and nine forced fumbles in three seasons.
Leonard congratulated Smith on his extension, tweeting: "Congrats my guy!!! Well deserved."
Nelson, who was the No. 6 pick in the 2018 draft, has a very good chance of becoming the highest-paid players at his position when he does get his extension. Nelson has been named an All Pro in each of his first three seasons in the NFL.
"Let me say this: We've had a great back and forth," Ballard said. "[Director of football administration] Mike Bluem has done tremendous, as all the agents we've been working with. They've been tremendous. It goes back and forth. Getting these early extensions done are not always easy but we'll continue to work through it."