Norman Cook, aka Fatboy Slim, said: "What a relief. I am glad common sense has prevailed.
"The team have a real chance of success and it is a real plus for the city."
Brighton and Hove's MPs reacted with delight at the news.
David Lepper, Labour MP for Brighton Pavilion, said: "It's excellent. The right decision has been made.
"Although some in Lewes might not like it, let's think about the many youngsters from the Lewes area who are going to benefit even more than they do at the moment from having a neighbouring club playing in a proper stadium and able to extend still further community activities across the Sussex area.
"This isn't just about Brighton and Hove Albion. It's about the impact of the club on sport in the region and economic development in the city."
Mr Lepper said the search for a new stadium for Albion had taken ten years - the length of time he had been in Parliament.
The campaign started when the club made the "unwise" decision to leave the Goldstone ground, when he was district and then city councillor.
Mr Lepper said: "Let's hope it is over now. This is the right decision.
All the other sites have been looked at.
"I would hope now is the time for Lewes District Council to say 'we have fought the fight and strung this out for something like five years now, spent however many thousands of pounds of taxpayers money, lost three Liberal Democrat seats on Lewes District Council at this year's election because of it - it's now time to accept the decision'."
The MP said Communities Secretary Hazel Blears, who made the final ruling, had delayed the decision to give her time to "genuinely consider all the pros and cons of the recommendations", following her recent appointment to the job.
He added: "She will be a welcome guest in Brighton and Hove in the near future."
Des Turner, Labour MP for Brighton Kemptown, when informed of the decision by The Argus, said: "That is wonderful news. Thousands of people in Brighton have been waiting for years for that.
"I'm glad all the efforts of the curmudgeons who were trying to stop this have come to nought.
"It's been a long road but the determination of fans helped keep things going when it looked difficult."
Dr Turner said the decision was "definitely a relief for Labour", but he added: "It's a quasi-judicial process so it's not right to have excessive political interference in it."
The MP said he was confident the decision would stand in the face of continued opposition from some quarters.
He said: "They'll be hard pressed to overturn it now. They have already slogged through a judicial review and the whole inquiry, I don't think they can do anything more. I don't think even Norman Baker would try that."
Celia Barlow, Labour MP for Hove, said: "This is a wonderful day for Brighton, Hove and Portslade.
"Although it took so long, it was only due to the commitment and faith of the club and the fans that we've got our stadium at last."
Norman Baker, Liberal Democrat MP for Lewes, said: "I'm not surprised at the decision."
Although ministers would say they had taken the decision on planning considerations alone, Mr Baker said he believed Labour Party politics in Brighton had "come into the matter".
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules hereComments are closed on this article