The linebacker had his left hand amputated when he was four, having been born with a condition that prevented the fingers from fully developing.
The 22-year-old joins his twin brother Shaquill, a cornerback, in Seattle.
Shaquem Griffin was in attendance in Dallas to hear his name called at the 2018 NFL Draft.
He starred at college level, winning his conference's defensive player of the year award in 2016 and playing in an unbeaten University of Central Florida team last season.
He gained attention at the NFL Combine in March when he ran the quickest 40-yard dash for a linebacker since 2003.
Griffin also bench-pressed 225lb 20 times, three more than his identical twin managed, having attached a prosthetic hand onto the bar. Current NFL defensive stars JJ Watt and Von Miller were among those to react in awe on social media.
He said before the draft: "I want to show the entire world, no matter [if you have] one hand, two hands, if you're a ball player, you just play ball."
University of Oklahoma quarterback Baker Mayfield, who won the Heisman Trophy for best college player, was the first pick of the 2018 draft on Thursday.
The Cleveland Browns chose Mayfield, 23, to kick off a draft considered one of the deepest in recent history for quarterbacks as four of the top 10 players taken were QBs.
Cleveland also had the fourth pick in the draft and chose to take cornerback Denzel Ward of Ohio State.
Penn State running back Saquon Barkley went second overall to the New York Giants, and University of Southern California quarterback Sam Darnold was selected third by the New York Jets.