Key, best known for his comedic roles, currently appears in musicals Jingle Jangle: A Christmas Journey and The Prom. The actor has also wrapped up production on another musical for Apple TV+.
"This was not part of the plan at all," Key told Corden while speaking with the late night host virtually on Tuesday.
The 49-year-old said he performed in musicals in high school but was always more interested in portraying characters and diving into their motivations.
"I always just wanted to get into the character part. That's what I always wanted to do. I was like, 'So what is the second gambler on the left in Guy and Dolls thinking though? What's his motivation?'' Key said.
"I was almost immediately going to go in a different direction and so the fact that it's come full circle like this is really fantastic. It's really fun," he continued.
Key stars as Streep's love interest in The Prom, a film about Broadway actors who try to help a lesbian student banned from bringing her girlfriend to prom. Corden, Nicole Kidman, Andrew Rannells, Kerry Washington and Tracey Ullman also star in the musical, from Ryan Murphy.
Key praised Streep and explained how easy it was to work with her in developing a scene.
"All of sudden she's not Meryl Streep anymore. She's just like a really fantastic acting partner and that's kudos to her because she makes an effort to make you feel comfortable. She wants you to be able to open up and be as brave and fearless as you can," Key said.