The Portsmouth South MP apologised in June last year for conducting an "inappropriate friendship" with a vulnerable female constituent.
He resigned from the Liberal Democrats in September after he had the whip removed but remained an MP.
The 68-year-old, who has battled health issues, said he hoped voters would accept he had paid for his "mistake".
Mr Hancock said he was still fit to do the job despite undergoing major heart operations and recently spending time at a mental health unit.
A civil action against him was dropped last year when the complainant agreed to a confidential settlement and the MP issued an apology.
He told BBC News: "I'm going to stand for sure, I've made this decision because my health is so much better and I think I owe it to a lot of people who have supported me.
"Once you've been an MP for as long as I have it's hard to just walk away.
"I think if enough people realise that I'm like everyone, I'm a fallible human being who made a mistake but paid a very high price for it... I think I could [win]."
He will go head-to-head with his former party colleague Gerald Vernon-Jackson who will be standing for the Liberal Democrats.
But Mr Hancock said he felt he "did not owe anything" to his old party and was not concerned about taking their votes.
He has been an MP in Portsmouth since 1984 and won with a majority of more than 5,000 votes in 2010.
He has also served as a Portsmouth councillor, which he carried out alongside his MP duties, until he lost his Fratton seat in the local elections last year.
Disgraced MP Mike Hancock has told BBC News he will stand in the general election as an independent candidate.