Brown has warned that the estimated £200 million in revenue promotion unlocks will be consumed faster than supporters expect.
Brown, speaking on BBC Radio 5 Live after Hull's 1-0 Wembley victory over Middlesbrough secured their return to the top flight for the first time since 2017, drew on his own experience of managing the club through their debut seasons in England's highest division.
"I don't want to state the £200 million but it does mean a lot of things," he said. "They can spend it all or they can spend it wisely. But I think the way the manager and the chairman are, they are very ambitious.
"They will want to survive in the Premier League. The money sounds great when you've won promotion but that money is going to get eaten up with transfers, wages and all of those things that play a big part in managing to survive."
He praised Oli McBurnie, whose 95th-minute header decided the match, as a forward whose value is often underestimated by those who judge on aesthetics rather than output.
"He doesn't carry the eye of being a great footballer but what a great scorer he is. A lot of people say about the way he plays, his body language and him as a person — but he has been very dominant aerially. If he is in the right area at the right time, he will put the ball into the back of the net to the benefit of his team."
Brown was unequivocal about what the promotion means for the city and the club.
"I think it is the best thing that can happen to Hull. They are classed as a yo-yo club but the best thing going forward for this club is survival in the Premier League next season."
Brown led Hull to promotion as Championship play-off winners in 2008 via a 1-0 victory over Bristol City at Wembley, Dean Windass scoring the only goal. He managed the club in their first ever Premier League season in 2008-09, when they finished 17th, and was sacked in March 2010 with the club in the relegation zone.
The wheel has turned again. This time the challenge is to make it stick.