Mr Hodgkinson's complaint will be sent to Cardinal Vincent Nichols, the head of the Catholic Church in England and Wales, the Papal Nuncio, the Pope's representative in the UK, and the Vicar General, one of the Church's most powerful figures, the Sunday Telegraph reported.
As well as stating Bishop Conry broke his celibacy vow, the complaint will say he has gone against Church teachings on adultery, marriage and family life by having a close relationship with Mrs Hodgkinson, a 43-year-old mother-of-two, and an affair with another married woman.
Mr Hodgkinson also claims the bishop abused his authority, taking advantage of both women after they turned to him for help with their marriages.
Graham Baldwin, from the charity Catalyst - which helps individuals whose family life has been affected by religious or cult groups - said: 'Bishop Conry has ... by his own admission on at least one occasion, committed adultery with a married woman, which in the eyes of the Church is a mortal sin.
'He needs to be laicised - what most people would understand as defrocked - and removed from the priesthood.'
Mr Hodgkinson, a 44-year-old banker, said: 'His behaviour has been appalling. To think that this is a person who people turn to for marriage advice is unbelievable. It makes him a hypocrite.'
Bishop Conry, 63, resigned as Bishop of Arundel and Brighton a fortnight ago, saying he had been 'unfaithful to my promises as a Catholic priest'.
He said it 'was the easiest way to avoid further embarrassment, disappointment...and shame for the church.'
In his resignation statement added that his actions 'were not illegal and did not involve minors.'
Despite this, the bishop insisted he wanted to remain in the Church as a priest.
Mr Hodgkinson discovered his wife's affair after she did not attend choir practice at their local church. He went to drop off some music through her letterbox to find she was not home at around 10pm.
He said: 'I thought it was really weird. I decided it was time to test my suspicion that she was having an affair.
‘I went up to the bishop’s residence and her car was there. I checked and it was there all night. I was devastated.’
Since then a second love affair with a married mother-of-three six years ago has come to light, and he has been linked to two other women.
Questions have been raised over whether the Catholic Church turned a blind eye to the bishop's behaviour.
After writing a letter to the bishop asking whether the pair were having an affair, Mr Hodgkinson did not receive a reply.
He then sent a second letter to the bishop, as well as the Papal Nuncio, the Vicar General and Cardinal Vincent Nichols, but none of them have responded.
Mr Hodgkinson said: ‘The thought of losing my wife to someone who has behaved so irresponsibly is awful.
‘He has abused his authority to the extent that he has allowed a married woman and mother of two children to sleep in his house and he has been completely blind to the emotional impact on the people affected by this.
‘For someone in his position to create that much emotional distress without really noticing or thinking about the consequences and then failing to explain himself is arrogant.
Conry technically remains both a priest and a bishop, even though he is no longer responsible for Arundel and Brighton.
