It’s taken a while, but Michael Buble has finally found himself. Stepping out of his Frank Sinatra/Rat Pack apprenticeship, the 29-year-old Canadian singer has matured into a first-rate contemporary artist. His performance Saturday at the Greek Theatre was a commanding display of entertainment skills, with well-crafted vocalizing as well as off-the-cuff humor.

Buble has always possessed the right stuff: good looks, a warm, engaging voice and an easygoing manner. What was missing before was a sense of individuality, the feeling of who he was, beneath his obvious affection for the Sinatra style.

His Saturday performance revealed how far he has come in the last couple of years. And most impressive was the fact that he has found his own voice, his own musical and professional persona, without having to abandon the more appealing elements he has absorbed from the Sinatra canon.

Buble sang, for example, “Come Fly With Me,” “For Once in My Life” and “I’ve Got You Under My Skin” in orchestrations distinctly reminiscent of the Sinatra versions, with a powerful sense of his own rhythmic lift. But he also did a humorous, spot-on Michael Jackson simulation, sang his own touching ballad “Home” (from his latest CD, “It’s Time”) and added impressive renderings of songs associated with other singers — “You Don’t Know Me” ( Ray Charles) and “A Song for You” (the Carpenters, Leon Russell).

Interacting closely with the capacity crowd, he joked with audience members near the stage and, at one point, leaped into an aisle, high-fiving and hugging people as he darted around the venue. At the end of the evening, he abandoned the microphone, connecting even more closely with the audience by singing the last phrases of “A Song for You” without amplification or accompaniment.

It was, by any measure, an impressive performance by an artist who is reviving the rich, popular-music qualities of emotion, lyricism and musicality that have dwindled in recent years. And he did so at the Greek in the company of a hard-swinging 12-piece band, playing orchestrations (many by John Clayton) affirming the still-potent qualities of the large jazz-band format.