Unbeaten Brook, 28, was fighting for the first time since he was stabbed in the leg while on holiday in Tenerife.
He dominated in his home town, flooring Dan four times before the Romanian failed to come out for the fifth round.
"I didn't think I would walk again, never mind box again. Now I'm here defending my title," said Brook.
"I've come from a council estate, now I'm world champion. I've come from the bottom and I'm at the top."
Dan, 33, had never been stopped in his previous 36 professional fights, but was sent to the canvas twice in the second round and twice more in the fourth before he was pulled out of the fight by his corner.
Brook, who has a perfect record of 34 wins from 34 bouts, was making the first defence of his world title since beating American Shawn Porter on points in California last August.
However, Brook's career looked to be over two weeks later when he was stabbed in the leg with a machete in what he called an "unprovoked attack".
"It was amazing to be able to walk to the ring again and this is where I belong," added Brook. "It was hard to hold it together. I didn't think I would box again, and I can't put into words what it means to defend my title."
Dan, born in Romania but based in Canada, was the mandatory contender but suffered only the third defeat of his 37-fight professional career.
Brook now hopes this win leads to an all-British bout with Amir Khan.
"If you're watching Amir Khan, then get in here with me. I know you're delicate around the whiskers," said Brook.
Promoter Eddie Hearn wants Brook to fight Khan at Wembley in June.
"There's a venue available on 13 June," said Hearn. "If Amir Khan is watching, give everyone what they want.
"He doesn't have an opponent and he is talking about fighting boxers lower than Kell. It's the biggest pay-day available and it's for a world title."
England's Kell Brook successfully defended his IBF world welterweight title with a fourth-round victory over Romanian-born Jo Jo Dan in Sheffield.