Woodward was born in Tullamore, County Offaly, Ireland. He trained as an engineer but developed an interest in medieval architecture, producing measured drawings of Holy Cross Abbey in County Tipperary. These drawings were exhibited at the RIBA in London in 1846.
The same year he joined the office of Sir Thomas Deane and became a partner in 1851 along with Deane's son, Thomas Newenham Deane. It seems that Deane looked after business matters, and left the design work to Woodward.
Woodward's two most important buildings are the Museum at Trinity College, Dublin (1854-1857) and the Oxford University Museum of Natural History, Oxford, (1854-1860). He was also responsible for the Kildare Street Club in Dublin (1858-1861) and Queen's College Cork, now University College Cork, (1845-1849).
The work of Deane and Woodward is characterised by naturalistic decoration with foliage and animals carved into capitals and plinths around windows and doors. It was extolled by John Ruskin in particular when he visited the Museum at Trinity College, Dublin. Woodward collaborated in particular with the O'Shea brothers. James and John O'Shea were stone carvers from County Cork. They, along with London sculptors, carved the abundant decorative stonework at Trinity, showing owls, lizards, cats and monkeys, as well as other flora and fauna. Later the O'Sheas carved stonework at the Kildare Street Club, including the famous window piece showing the club members as monkeys playing billiards. Woodward shared Ruskin’s ideal of wanting the Oxford Museum to mark a return to the Gothic tradition of enriching the structural forms with naturalistic symbolism – drawing inspiration from real plants and animals. To realise this he was willing to let his craftsmen improvise their own solutions to problems, just as mediaeval stonemasons apparently did. Despite suffering from the tuberculosis that was to kill him in 1861, Woodward quickly became a charismatic presence in Oxford, as W. Tuckwell recalled: ‘Then into our midst came Woodward … a man of rare genius and deep artistic knowledge, beautiful in face and character, but with the shadow of an early death already stealing over him.’ Among his admirers were Gabriel Rossetti, Burne-Jones, and William Morris and while in Oxford he was also commissioned to design the new Oxford Union building – upon which the Pre-Raphaelites were to become famously involved in painting the frescoes. Woodward brought with him from Ireland a team of carvers and stone masons, who lived in a temporary camp erected at the site – which included an institute, complete with reading room and lecture hall. It was here that Ruskin addressed the workmen in April 1856, setting out his theories of Gothic architecture and the creative role of the ordinary craftsmen in making it a reality. This ideal of the artist-craftsman found its realisation in the O'Shea brothers. Ruskin was (at first) highly charmed by the ebullient and talented O’Sheas, and their naturalistic approach to carving capitals and windows chimed perfectly with Ruskin’s mediaeval vision. Tuckwell describes how ‘every morning came the handsome red-bearded Irish brothers Shea, bearing plants from the Botanic Garden, to reappear under their chisels in the rough-hewn capitals of the pillars.’
 Rev. W. Tuckwell, Reminiscences of Oxford (1901), p. 48.  Tuckwell, Reminiscences, p. 49.
- Dodgson, Campbell (1901). Dictionary of National Biography (1st supplement). London: Smith, Elder & Co. .