The Seagulls hope to move from their 6,500-capacity temporary home at Withdean into their new home by 2008 after being without a home since the Goldstone Ground was sold by the previous owners in 1997. They have been playing at the ill-suited athletics stadium since 1999 following a groundsharing spell at Gillingham.
McGhee, preparing for today's home game with Ipswich, told the club's website: "That there's going to be a new stadium is unbelievably good news for both the football club and the city. I suspect even the supporters might not fully appreciate the impact the new stadium will have.
"It excites me and my mission is to be the manager who takes us into that new stadium. On the back of this fantastic news about the new stadium at Falmer, things are looking good at this football club.
"I've gone on record before as saying it was important to get the new stadium for the club to survive financially and, in the name of common decency, the fans needed a roof over their heads."
There was also a message of goodwill from Championship rivals Coventry City, where former Brighton manager Micky Adams, who led Albion for two and a half years, is now in charge.
"This is fantastic news and I'm delighted for the fans down there on the south coast," Adams said.
"When I was Brighton manager we were groundsharing at Gillingham and the supporters were making 140-mile round trips just to watch their team play. The club have already done fantastically well to survive on gates of 6,000 at Withdean. But now the Premiership is not out of the equation, is it?"
The Seagulls chairman, Dick Knight, said: "This is the greatest home win ever in the club's history. Brighton deserves a stadium and we've been very patient because it's been the longest-running inquiry in football history.
"We campaigned very hard. There's been a lot of hard work gone into this project over the course of the last seven years and we've really been through the mill but that just makes it all the sweeter.
"Never mind over the moon, we're over Jupiter."