The winger impressed during the second half of the campaign, with performance-related criteria in the deal triggering a permanent transfer.
The Ecuador international made 21 appearances for Brighton after joining the club in 2021, but spent much of his time away on loan to gain experience.
During that period, he had spells with West Bromwich Albion, Ipswich Town, Burnley and Cremonese.
“Jeremy has spent the last few years out on loan, so this represents a great opportunity for him to settle in one place,” said Brighton technical director Mike Cave.
“He is another success story of a player joining our under-21s and making the step up to men’s football at a very good level. We wish him the best of luck for the future."
Sarmiento has twice achieved promotion from the Championship, with both Ipswich and Burnley, and played a key role in Middlesbrough’s push to last season’s play-off final.
The 24-year-old now begins a new permanent chapter at the Riverside Stadium as Boro strengthen their attacking options.