Sam, the joint defensive player of the year in the Southeastern Conference who announced in February he was gay, would become the first openly gay player in the NFL should he make the team's 53-man regular -season roster this summer.
Sam was taken on the 249th pick in the last round of the three-day draft at Radio City Music Hall.
Television cameras captured Sam receiving the telephone call informing him of his selection, the Texan breaking into tears and shaking with joy at the news.
"Thank you to the St Louis Rams and the city of St Louis," he tweeted. "I'm using every ounce of this to achieve greatness!!"
Jeff Fisher, the St Louis Rams coach, said: "I'm excited about our draft and excited about the possibility of adding him to our defensive front. After doing the studies, he's a good football player."
Sam would become the second openly gay player in one of North America's four major professional team sports following basketball's Jason Collins, who joined the NBA's Brooklyn Nets this season.
"I think it's a great day for the NFL and for Michael and his family," Collins said, before taking the court for the Nets' play-off game against the Miami Heat.
Asked about the wider significance of the day, Collins added: "It takes more and more people just to come forward. We're normal people and we're just trying to make plays to make our respective teams win."
Fisher said he was unconcerned about a possible media scramble to cover Sam at training camp or about any problems within the clubhouse over welcoming a gay player. "I don't have any concern," he said. "There's going to be a little extra attention for a couple of days but ... we're looking forward to this opportunity. We're not going to let any kind of distractions affect this team."