Denis was born in Shanagolden in County Limerick, Ireland.

He arrived with his brother, Timothy and sisted Bridget, on 2 February 1852 on the Adelaide. They paid their own passage and were not assisted immigrants. They gathered at Belvidere, near Greenock with shipmates and other new friends. Later they sent for their sisters, who managed to secure life partners on the voyage.

On 6 February 1855, Denis married Bridget Browne, daughter of Andrew and Mary Browne of Saddleworth, at St. John's Church, Kapunda and settled on their small acreage at Belvidere, near brother Thomas and his wife Ellen. During 1858, Denis and Bridget decided to sell their small property and moved north to Mintaro, where they had acquired another farm.

Madigan's farm was located one mile north of Mintaro, on the road to Farrell Flat, about the same distance from the Church of the Immaculate Conception, where the family regularly attended Sunday Mass. The children most likely attended Mr. Horan's school, situated about three miles to the north and then the Sisters of St. Joseph, when they commenced a school at the Catholic Church. One of the boys, Thomas, continued his education at the Jesuit College at Sevenhill.

By 1885, Denis had increased his holding to include Sections, 121, 122, 127, 128, 133 and 281 Hundred of Stanley, consisting of 419 acres. Denis also grew several grape vines on his farm, from which he was reputed to have made wine in his cellar. One occasion, which many people of the district could remember for a long time, was when Denis made a large bonfire in honour of Dan O'Connell, a famous Irishman, and all the friends in the district were invited and a huge gathering attended the event.

Members of the Madigan family were known for their singing. Mary, the eldest child, was the choir mistress of the Church of the Immaculate Conception for a number of years, having played the organ since she was aged 12. She was greatly missed when she married and left the district in 1877. Her brother Tom was also known to have a good voice, and, when other family members joined in, the choir was appreciated by all parishioners.