The wing back had been on Adams wanted list but opted to go to Kenilworth Road after building up a relationship with Mike Newall.
Edward's agent Mike Berry told SkySports.com: "He will sign for Luton, effectively it will be the 1st of July, but we've agreed personal terms and he's looking forward to joining the club.
"We turned down Plymouth last Friday, and also Coventry, but he also had Sheffield Wednesday and Leeds, he had numerous Championship clubs chasing him.
Mike Newell's been watching him for three years and he has a good rapport with the manager and Mike Newell made him very welcome at the meeting and the chairman was very ambitious and they just said all the right things you know."