Sam played for the University of Missouri Tigers, and came out as gay in media interviews earlier this year. His team and coaches knew his secret and kept it for his final college season.
He went on to have the best year of his career and was the Southeastern Conference (SEC) defensive player of the year.
The 6ft 2in, 255lb Sam was considered a mid-to-late round pick, far from a sure thing to be drafted.
Sam was selected in the seventh and final round and admitted it was a frustrating wait. He said teams that passed on him chickened out and he should have been drafted sooner.
"From last season alone, I should've been in the first three rounds. SEC Defensive Player of the Year, All-American," Sam said. He stopped short of directly saying his stock dropped in the draft because he came out.
"You know what, who knows? Who knows? Only the people who sit in the war room know," he said. "They saw Michael Sam, day after day they scratched it off the board. That was their loss.
"But St Louis kept me on that board. And you know what I feel like I'm a (Jadeveon) Clowney, a first draft pick. I'm proud of where I am now."
The pick came after several rounds of suspense. The first round of the day, No 4 overall, came and went, no Sam. Then the fifth and sixth, and finally, the day was down to just a handful of picks.
When Mike Kensil, the NFL's vice president of game operations, walked to the podium at Radio City Music Hall in New York in the draft's final minutes to announce the Rams' second-to-last pick, the crowd got a sense something was up. Very few of the last day picks were announced at the podium. Twitter lit up with suggestions the Rams were about to make news.
When Mr Kensil said: "The St Louis Rams select ... Michael Sam..." the fans gave a hearty cheer, chanting "Yes! Yes! Yes!" and "Michael Sam!"
Sam was in San Diego watching with friends and family at the home of his agent, Joe Barkett of Empire Athletes. ESPN and the NFL Network had cameras there and showed Sam's reaction.
Sam was on the phone, with his boyfriend hugging him and rubbing his left arm. When Sam got off the phone, the tears started. He gave his boyfriend a big kiss and a long hug as he cried and his eyes reddened. After, they shared cake - and another kiss.
"Thank you to the St. Louis Rams and the whole city of St Louis. I'm using every once of this to achieve greatness!!" Sam tweeted with a frenzied typo moments after he was picked, with a picture of himself wearing a Rams cap and a pink polo shirt.