Dwyer was born in Camara, a townland in the Glen of Imaal County Wicklow. He was the eldest of seven children of farmer John Dwyer and his wife Mary (née Byrne), who had a farm in the widespread fields of Wicklow and supplied the men of the rebellion with food. In 1784 the family moved to a farm in Eadestown. Dwyer was a cousin of Anne Devlin, who would later achieve fame for her loyalty to the rebel cause following the suppression of Robert Emmet's rebellion.
Dwyer joined the Society of United Irishmen and, in the summer of 1798, he fought with the rebels as captain under General Joseph Holt in battles at Arklow, Vinegar Hill, Ballyellis and Hacketstown. Under Holt's leadership, he withdrew to the safety of the Wicklow Mountains in mid-July, when rebels could no longer operate openly following their defeat in the disastrous midlands campaign. Dwyer and Holt tied down thousands of troops.
Dwyer and his men began a campaign targeting local loyalists and yeomen, attacking small parties of the military and eluding any major sweeps against them. His force was strengthened by many deserters from the military, who headed to Wicklow as the last rebel stronghold and who became the dedicated backbone of his force, as they could not be expected to be included in any future offer of amnesty.
Due to the constant hunt for him, Dwyer was forced to split and reassemble his forces and hide amongst civilian sympathisers to elude his pursuers. On 15 February 1799 at Dernamuck, he and about a dozen comrades were sheltering in three cottages when an informer led a large force of the British soldiers to the area. The cottages were quickly surrounded, the first two surrendering, but, following consultation, Dwyer and his men decided to fight on in the third one, Miley Connell's cottage, after negotiating the safe passage of women and children. In the hopeless gunfight which followed, the cottage caught fire and only Dwyer remained unwounded. At this stage, Dwyer's comrade, Antrim man Sam McAllister, stood in the doorway to draw the soldiers' fire on him, which allowed Dwyer to slip out and make an incredible escape.
Dwyer later made contact with Robert Emmet and was apprised of plans for his revolt but was reluctant to commit his followers to march to Dublin unless the rebellion showed some initial success. The subsequent failure of Emmet's rising led to a period of repression and renewed attempts by the Government to wipe out Dwyer's forces. Methods adopted included attempts to deny him shelter among the civilian population by severely punishing those suspected of harbouring his men, the offer of huge rewards for information, the assigning of thousands of troops to Wicklow, and the building of a series of barracks at Glencree, Laragh, Glenmalure and Aghavannagh and a military road through county Wicklow.
In December 1803, Dwyer finally capitulated on terms that would allow him safe passage to America but the government reneged on the agreement, holding him in Kilmainham Jail until August 1805, when they transported him to New South Wales (Australia) as an unsentenced exile.
Dwyer arrived in Sydney on 14 February 1806 on the Tellicherry and was given free settler status. He was accompanied by his wife Mary and their eldest children and also by his companions, Hugh 'Vesty' Byrne and Martin Burke, along with Arthur Devlin and John Mernagh. He was given a grant of 40.5 ha (100 acres) of land on Cabramatta Creek in Sydney. Although he had originally hoped to be sent to the United States of America, Michael Dwyer was later quoted as saying that "all Irish will be free in this new country" (Australia). This statement had been used against him and he was arrested in February 1807 and imprisoned. On 11 May 1807, Dwyer was charged with conspiring to mount an Irish insurrection against British rule. An Irish convict stated in court that Michael Dwyer had plans to march on the seat of Government in Australia, at Parramatta. Dwyer did not deny that he had said that all Irish will be free but he did deny the charges of organising an Irish insurrection in Sydney. Dwyer had the powerful support of Australia's first Jewish policeman, John Harris, who expressed the opinion in court that he did not believe that Dwyer was organising a rebellion against the Government in Sydney. On 18 May 1807, Dwyer was found not guilty of the charges of organising an Irish insurrection in Sydney.
Governor William Bligh disregarded the first trial acquittal of Michael Dwyer. Bligh who regarded the Irish and many other nationalities with contempt, organised another trial for Michael Dwyer in which he was stripped of his free settler status and transported to Van Diemens Land (Tasmania) and Norfolk Island. After Governor Bligh was overthrown in the Rum Rebellion in 1808, the new Governor of New South Wales, George Johnston, who was present at Dwyer's acquittal in the first trial, ordered that Michael Dwyer's freedom be reinstated. Michael Dwyer was later to become Chief of Police (1813–1820) at Liverpool, New South Wales but was dismissed in October for drunken conduct and mislaying important documents. In December 1822 he was sued for aggrandising his by now 620 acre farm. Bankrupted, he was forced to sell off most of his assets, which included a tavern called "The Harrow Inn", although this did not save him from several weeks incarceration in the Sydney debtors' prison in May 1825. Here he evidently contracted dysentery, to which he succumbed in August 1825.
Originally interred at Liverpool, his remains were reburied in the Devonshire Street Cemetery, Sydney, in 1878, by his grandson John Dwyer, dean of St Mary's Cathedral. In May 1898 the coincidence of the planned closure of the cemetery and centenary celebrations for the 1798 rebellion suggested the second re-interment of Dwyer and his wife in Waverley Cemetery, where a substantial memorial was erected in 1900. The massive crowds attending Dwyer's burial and the subsequent unveiling of the monument testified to the unique esteem in which Irish-Australians held the former Wicklow hero.
Dwyer had seven children and has numerous descendants throughout Australia. In 2002, in Bungendore near Canberra, a family reunion took place, with Michael Dwyer's descendants joining descendants of related Australian Irish families, the Donoghoe's and the Doyles. In 2006, a reunion also took place to mark the 200th anniversary of the arrival of the Tellicherry in Botany Bay. One of Michael Dwyer's sons was the owner of The Harp Hotel in Bungendore, New South Wales in circa 1838. Dwyer's nephew, John Donoghoe (1822–1892), built The Old Stone House, Molongolo Rd, Bungendore, in circa 1865. This dwelling is a strongly constructed Bungendore landmark and a monument to pioneering and hard-working Irish Australian settlers.
'Dwyer's Cottage', or the 'Dwyer–McAllister Cottage', as it is more formally known, was acquired by the Irish State from the Hoxey family in 1948. President Seán T. O'Kelly was present at a ceremony to mark the occasion.
At least two Gaelic Athletic Association clubs bear Dwyer's name: Keady Michael Dwyer's GFC is a club in County Armagh, and Michael Dwyers is a juvenile club in County Wicklow.
Micheal Dwyer is depicted as one of the few survivors of Vinegar Hill in the 2015 American musical "Guns of Ireland".