[3][4] In 2007, he had made his role debut as Arnold with Antonio Pappano conducting the Orchestra and Chorus of the Accademia Nazionale di Santa Cecilia, a role he has since repeated at the Royal Opera House in London, Theater an der Wien, Grand Théâtre de Genève, Dutch National Opera, Opéra de Lyon, Wiener Staatsoper, Teatro Regio di Torino and his debut at Carnegie Hall with Gianandrea Noseda.

[5] Osborn has sung the title of role of Rossini's Otello at the Opéra de Lausanne, Teatro San Carlo in Naples, and also in Tokyo, Vienna, Paris, Lyon, Zurich and at the Salzburg Festspielhaus, among other venues.

[9] Osborn is the recipient of the 2011 Goffredo Petrassi Award for his contributions to Italian culture,[5] 2012 Aureliano Pertile Award in Asti, Italy for his portrayal as Roméo at the Arena di Verona; 2014 Premio Bellini D’Oro in Catania, Sicily for his Elvino in Bellini's La sonnambula in Bari's Teatro Petruzzelli and Alfredo Germont in Verdi's La traviata at the Arena di Verona; 2016 "Prix d’Amis" from the Friends of the Dutch National Opera for his performances as Cellini in Benvenuto Cellini; the Italian “Franco Abbiati” Critics Award for best Male Singer for his critically acclaimed performances as Fernand in Donizetti's La favorite at La Fenice, Cellini in Benvenuto Cellini at Teatro dell’opera di Roma, and his Otello at the Teatro San Carlo di Napoli in the season 2016; and most recently the Italian "Oscar della Lirica" from Fondazione Arena di Verona in the category of "Best Tenor" 2016/17 (Awards Ceremony held in Haiku, Hainan, China).

Audio recordings include Tribute to Gilbert Duprez with Constantine Oberlian and the Kaunas Symphony Orchestra on Delos Records, L'amour consacré and La coppia degli acuti with wife and soprano, Lynette Tapia, Christopher Larkin conducting the English Chamber Orchestra;[10] Guillaume Tell (the complete French version) with Antonio Pappano and the Accademia Nazionale di Santa Cecilia; and Bellini's Norma for Decca with Cecilia Bartoli, Sumi Jo, and Michele Pertusi, and Rossini's Semiramide from the Rossini Festival Bad Wildbad on Naxos, and Meyerbeer's Robert le diable.

Video recordings include the Halevy's Clari (DVD: Decca); Rossini's Armida (The Met Live in HD: Decca); and Bellini's I puritani (DVD: Opus Arte), Benvenuto Cellini staged by Terry Gilliam (TV), and also Les contes d'Hoffmann with Dutch National Opera, staged by Tobias Kratzer; and also one by Laurent Pelly (Opéra de Lyon Japan Tour's televised by NHK).