They spent a sleepless night together before phoning the lottery operator, Camelot, at 8am to verify the win.
"We celebrated with a hug and a cup of tea... then wrote a list of those we would share it with", they added, saying they meant to give some of their winnings to fifty people.
Commenting on the win, he said, "I've got a wonderful wife, a wonderful family and wonderful friends, so this is the icing on the cake".
The couple are the biggest EuroMillions winners on the island of Ireland, after eclipsing Dolores McNamara's €115m win in 2005.
The couple now live in a rented home and were considering a move to Croydon in March, as Mr Connolly had been offered a new job as an operations manager, but since finding out about the win he has chose to retire.
Frances and Patrick Connolly from Moira. "The pleasure for me is going to be seeing their faces".
The 52-year-old said they have already made a list of people they want to give the money to.
Mr Connolly is a businessman and Mrs Connolly is a teacher, who has been off work for a period of time due to a leg injury.
"It's going to be so much fun giving it away", she said.
Asked whether she would have to increase her personal security, she joked: "I've never met anybody I couldn't take down myself, to be fair".
A huge mansion is not on the cards though, Ms Connolly explained.
"There's no way I'm joining the jet set."
"There are no skeletons, there are no dirty pictures, there is not enough to keep us in the public eye".
Before going to bed, he checked the result and found they had the winning numbers: 01, 08, 11, 25, 28, with lucky stars 04 and 06.
A ticket sold in Beaumont in Dublin in 2013 was worth €94m.
EuroMillions is played in nine countries - the UK, Austria, Belgium, France, Ireland, Luxembourg, Portugal, Spain and Switzerland - with ticket-holders trying to win a share of the same jackpot.