The £65m arena is due to have a pre-launch event with Bruce Springsteen on 24 July. Elton John is set to officially open the 13,000-seat venue on 4 September.
John Sutherland, managing director of SMG Europe, said: "SMG Europe is totally committed to operating world-class arenas that are supported by world-class commercial partnerships."
Mark Mullen, chief executive of First Direct, added: "Leeds is the city that has made us who we are and we’re thrilled to be able to support such a major development for all the people who live and visit here."
The news comes three months after to provide the security and crowd control services at its mainland venues in England.
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