The Missouri defensive end became the first openly gay player to be drafted in league history and seeks to be the first openly gay athlete ever to play in the NFL.
Video of Sam receiving the call from the Rams and coach Jeff Fisher revealed the player's emotion while surrounded by friends, family and his boyfriend.
Sam's emotion carried over into a conference call with the St. Louis media.
"Let me tell you something, if we were playing the Vikings right now, I'd probably have three sacks the first game," Sam said. "Since February and my big announcement, this has been a whole [lot of] speculation of the first openly gay football player, but you know what? It's not about that. It's about playing football.
"Can Michael Sam play football? Yes, I can, and the St. Louis Rams know I can. I am going to give everything I've got to the St. Louis Rams to help the Rams win a championship."
Sam added in a statement: "The moment my name was called was the single greatest moment of my life."
For the Rams, drafting Sam added another significant moment in franchise history that has little to do with sports.
In 1946, a year before Jackie Robinson signed with the Dodgers, the Rams signed Kenny Washington, the first African-American football player in the modern era of the NFL.
That fact was relayed to Fisher not long before the Rams turned in the card with Sam's name. It's a legacy in which Fisher takes pride.
"This is the second historic moment in the history of this franchise," Fisher said. "From that standpoint, from a historic standpoint, I'm honored to be a part of that."
The White House released a statement expressing congratulations from President Obama.
"The President congratulates Michael Sam, the Rams and the NFL for taking an important step forward today in our Nation's journey," the statement, which a White House official emailed to ABC News, read. "From the playing field to the corporate boardroom, LGBT Americans prove everyday that you should be judged by what you do and not who you are."
All along, Sam insisted that he wanted to be known simply as a football player and not as some sort of trailblazer. Now he'll get the chance just a couple of hours down the road from his college home in Columbia, Missouri.
Sam announced that he is gay on ESPN before February's NFL scouting combine. The 6-foot-1, 261-pound Sam earned SEC Defensive Player of the Year honors in 2013 after posting 11.5 sacks and 19 tackles for loss.
At the Senior Bowl in January, Sam worked out at outside linebacker after playing as a defensive end in Missouri's 4-3 scheme. That experiment appeared to hurt Sam's stock to the point where many believed he might not get drafted.
As Friday melted into Saturday and the picks dwindled away, Fisher and general manager Les Snead began considering Sam as a possibility. By the time they were to pick in the seventh round, Sam stood above most players remaining on their draft board.
Two picks before the Rams came on the clock with their two seventh-round compensatory selections, Fisher and Snead had private conversations with chief operating officer Kevin Demoff and owner Stan Kroenke about choosing Sam.