The Rays acquired Vasil from the Phillies on Wednesday in exchange for cash considerations.
The Phillies selected Vasil with the 14th pick in the Rule 5 draft Wednesday, JJ Cooper of Baseball America reports.
Vasil is a candidate to replace Tylor Megill (shoulder) in the Mets' rotation, Will Sammon of The Athletic reports.
Vasil is expected to open the season in the minors rather than compete for a rotation spot in the wake of the Kodai Senga (shoulder) injury, Tim Healey of Newsday reports.
The Mets promoted Vasil from Double-A Binghamton to Triple-A Syracuse on Monday, Tim Healey of Newsday reports.
Vasil has a 2.70 ERA, 0.70 WHIP and a 41:4 K:BB in 30 innings across six starts for Double-A Binghamton.
The Mets promoted Vasil from Single-A St. Lucie to High-A Brooklyn on Monday.