Smith completed 64.3 percent of his passes for 18 touchdowns and five interceptions last season. He also rushed for 264 yards and four scores.
The Pats will be without six-time Super Bowl champion Tom Brady under center for the first time in two decades next season.
Right now, the leader to replace him appears to be second-year pro Jarrett Stidham, whom the Pats took in the fourth round of the 2019 draft out of Auburn. Veteran Brian Hoyer rounds out the quarterback depth chart, which did not see any additions during the 2020 draft.
New England also has the option to pursue a quarterback in free agency. Of note, two former No. 1 overall draft picks in free agents Cam Newton and Jameis Winston are still without homes.
Stidham looks like the clear-cut starter, though, to the point where ESPN's Mike Reiss wondered whether he was the "Biggest winner of the Patriots' 2020 draft."
When asked whether the Pats' decision not to draft a quarterback indicated his feelings on Stidham and Hoyer, Pats head coach Bill Belichick said the following (h/t Ryan Hannable of WEEI): "Yeah, I like both those players. ... I have confidence in both of those players."
The signs have pointed toward Stidham being QB1 for a while, with Jeff Howe of The Athletic writing the following on April 1:
"At this point, a source has said the Patriots have expressed no interest in signing Cam Newton or trading for Andy Dalton — the two most popular speculated moves — nor do they have the cap space to make such a transaction.
"So it'll be Stidham. It'd hardly be a surprise if they open camp with Hoyer as the starter and force Stidham to wrest away the job, but a dose of adversity should help the kid if that's the route they choose. Either way, as long as Stidham maintains his pace from last summer, it should be his job."
Pats' director of player personnel Nick Caserio indicated Friday after Round 3 that the team would be looking to add a third quarterback to the roster, and Belichick remarked Saturday that the new signal-caller would be a UDFA but did not confirm the Smith signing.
But Smith appears to be the pick, however, as the Pats embark on the first year of the post-Tom Brady era.