This is the third time Verlander has finished second in Cy Young voting during his 14-year career.
The 25-year-old Snell becomes the youngest pitcher to claim the award since Clayton Kershaw in 2011 after leading the rotation of a Rays club that finished 2018 with a 90-72 record.
"Man, this is crazy, hard to put into words!" Snell posted on Instagram after learning he'd won. "But, just wanted to say thank you to all the people who supported me, the love is felt! This is just the beginning and I'm so thankful for you all!"
Snell's 180 2/3 innings pitched were also the fewest from a Cy-Young-winning starter over a full season, according to the BBWAA.
Snell completed the regular season with a 21-5 record and was tops in the AL with a 1.89 ERA.