The agency will help re-establish the venue's credentials as an organiser of major events via a PR campaign targeting both the music industry and potential gig-goers.
The overhaul is part of the redevelopment of the whole Wembley site, most notably including the new national football stadium.
The arena's refurbishment, creating an increased 17,000 capacity, sees much of the original 1930s design reclaimed.
Depeche Mode is one of the first acts confirmed to play at the new venue, with a show lined up for next April.
The site currently houses a temporary, 10,000-seat venue called The Pavilion.
Outside senior press officer Peter Berry leads a four-strong account team, reporting to sales and marketing director Peter Tudor.
- Separately, Outside has scooped a UK PR contract to promote US rock band Bon Jovi. The group has formerly been promoted in the UK by LD Publicity.