The 45-year-old Rea, who was head coach of the Londoners from 2000-06, returned from Australia to take charge of the last seven matches of the season and has now signed a two-year contract.
Broncos chairman David Hughes said: "We've had lots of applications and have given them all due consideration but I think Tony Rea is the man for the job."
The announcement represents a change of heart by Rea, who initially returned to the club as a favour for Hughes and insisted he had no intention of making the appointment permanent.
However, after masterminding three consecutive victories, including a 62-18 rout of Challenge Cup finalists Warrington last Friday, the former Brisbane Broncos hooker was happy to perform a U-turn when offered the position by the chairman.
"He came sat me down and asked me to think about it and it was purely a coaching decision," Rea said. "If I scratch myself hard enough, I did miss coaching."
Rea, who spent 13 years at the Broncos after joining them as a player from Brisbane in 1994, is synonymous with the club's most successful era. He was their chief executive when they finished as Super League runners-up to Bradford in 1997 and reached the Challenge Cup final two years later and, as coach, took them to the play-offs in 2003 and 2005.
Rea left London at the end of 2006 - to be replaced by Brian McDermott, who was subsequently succeeded by Powell four years later - and joined Australian rugby union team the Brumbies. Since leaving the Brumbies last year, he has been working in the business world as a performance coach but responded last month to an SOS from Hughes, who decided to part company with Powell with the Broncos bottom of Super League.
Hughes said: "One shouldn't underestimate what a tough task it is coaching a club like the London Broncos but I think Tony Rea is the man for the job."
"I believe in his coaching. His prowess has strengthened in his time away from us."
- Tony Rea