The tackle was traded from the Jacksonville Jaguars to the Super Bowl champions earlier this week.
The 26-year-old told reporters: "I was sitting at home on my iPad reviewing film, getting ready for St Louis, and my agent calls me and he's like, 'I need you to sit down. I've got to talk to you about something'. And I was like, 'You've got to be kidding me'.
"But it happened, and it happened quick. It's an exciting change for me. I'm definitely glad to be here, glad that I was sought out, definitely appreciative of that. For me, it's just an awesome opportunity.
"I know what [the Jaguars are] building down there, and it'll come. But to come into a situation like this with a culture of winning is unique. It's something that I really haven't been around, so it's exciting to experience this."
Monroe was a first-round Draft pick in 2009.