Mullen, who won £4.8 million on the lottery in 2011, will be a director of the National League North club.
"Lee's joining with an initial stake that he is comfortable with, that could grow" Bradley told BBC Radio Derby.
Mullen is a former director of his local club Grimsby Town, where he was also an investor, helping them into the football league in 2016.
"I'm delighted we've brought in a new board member who's going to invest in the football club and I'm hopeful he will be instrumental in the latest saga of us looking to continue in a spiral upwards" Bradley added.
"Lee's coming in with huge enthusiasm to do the job and with a huge breath of fresh air."
As part of the investment, Bradley had to let manager Russ O'Neill go.
"Whilst all decisions are difficult, I think this is a positive one and the right one at this time," Bradley said.
"I hope we're going to build a side that will be full of guts and desire and be good enough to compete with the best in the division."
Alfreton Chairman Wayne Bradley says that new director and investor Lee Mullen will be "a breath of fresh air".