Raised and educated in Vestal, New York, he attended Eastman School of Music but dropped out after a semester.
Leech made his debut at the New York City Opera in 1984 as Rodolfo in La bohème.
On March 25, 1987, Leech began a two-decade affiliation with Cincinnati Opera with his debut as Hoffmann in Les contes d'Hoffmann.
Leech established himself as one of the world's leading tenors in lyric roles such as Edgardo, Duke of Mantua, Alfredo, Faust, Roméo, Hoffmann, des Grieux, Werther, Pinkerton, et al. Possessing a beautiful clear voice with a thrilling upper register, was compared to Jussi Björling and Luciano Pavarotti by critics.
In 2015, he began a new affiliation with Michigan Opera Theatre as Director of Resident Artist Programs.