Thomas was the son of Thomas Sandby Senior of Babworth in Nottinghamshire who took up his residence at Nottingham early in the eighteenth century. Paul Sandby, the landscape artist, was his brother. The Sandbys of Babworth are said to have been a branch of the family of Saundeby or De Saundeby of Saundby in Lincolnshire. As a draughtsman and architect, Thomas Sandby was self-taught. At the Nottingham Museum is a drawing by him of the old town-hall at Nottingham, dated 1741, and a south view of Nottingham, dated 1742; and Deering's ‘History of the Town’ contains engravings of the castle and town-hall, after drawings executed by him in 1741.

According to the ‘Memoirs’ of James Gandon the architect (1846), he and his brother Paul kept an academy in Nottingham before they came up to London in this year, although this seems unlikely. They were then of the respective ages of twenty and sixteen. According to Antony Pasquin (John Williams), in his ‘Memoirs of the Royal Academicians’ (1796), Thomas Sandby came to London for the purpose of having a view of Nottingham engraved, which had been executed on principles of perspective perfected by himself, and had won him reputation in his native town. According to Gandon, on the other hand, both he and his brother left Nottingham in order to take up situations in the military drawing department at the Tower of London, which had been procured for them by John Plumptre, the Nottingham MP. In 1743, Sandby was appointed private secretary and draughtsman to Prince William Augustus, Duke of Cumberland, and accompanied him on his campaigns in Flanders and Scotland (1743–1748). Sandby was at the Battle of Dettingen in 1743. Pasquin says that he was appointed draughtsman to the chief engineer of Scotland, in which situation he was at Fort William in the Highlands when the Pretender landed, and was the first person who conveyed intelligence of the event to the Government in 1745. He accompanied the Duke on his expeditions to check the Rebels, and made a sketch of the Battle of Culloden which is now in the Royal library at Windsor Castle, together with three panoramic views of Fort Augustus and the surrounding scenery, showing the encampments, in 1746, and a drawing of the triumphal arch erected in St. James' Park to commemorate the victories. In this year, the Duke was appointed Ranger of Windsor Great Park, and selected Sandby to be Deputy Ranger; but Sandby, again, accompanied the Duke to the War in the Netherlands, and probably remained there till the conclusion of the peace of Aix-la-Chapelle in October 1748. In the British Museum are four views by Sandby of the camps in the Low Countries, covering extensive tracts of country, and another inscribed ‘Abbaye près de Sarlouis.’ Two of the former are dated 22nd June 1748, and in the Royal Collection at Windsor is a very elaborate drawing of ‘Diest from the Camp at Mildart, 1747.’

His appointment as Deputy Ranger of Windsor Great Park, which he held till his death, placed Sandby in a position of independence, and afforded scope for his talent both as an artist and as an architect. The Great Lodge (now known as Cumberland Lodge) was enlarged under his supervision as a residence for the Duke. The Lower (or Deputy Ranger's) Lodge (now the Royal Lodge) was occupied by himself. His time was now principally spent in extensive alterations of the Park, and in the formation of the Virginia Water, in which he was assisted by his younger brother, Paul, who came to live with him. A number of his plans and drawings illustrating these works are preserved in the Royal library at Windsor Castle and in the Soane Museum. In December 1754, a prospectus, etched by Paul Sandby, was issued for the publication of eight folio plates, dedicated to the Duke of Cumberland, illustrating the works at Virginia Water. They were drawn by Thomas Sandby and engraved on copper by his brother, Paul, and the best engravers of the day. A number of the original plans and designs for these works are also preserved at Windsor Castle and the Soane Museum. George III, who took great interest in the undertaking, honoured Sandby with his confidence and personal friendship and, on the death of William Augustus, Duke of Cumberland, in 1765, the King's brother, Henry Frederick, the new Duke of Cumberland, and Ranger of the Park, retained Sandby as his deputy.

Although devoted to his work at Windsor and preferring a retired life, it was Sandby's custom to spend a portion of each year in London. He rented a house in Great Marlborough Street from 1760 to 1766. He was one of the committee of the St. Martin's Lane School, which issued a pamphlet in 1755 proposing the formation of an academy of art, and he exhibited drawings at the Society of Artists' Exhibition in 1767, and afterwards for some years at the Royal Academy. Both he and his brother, Paul, were among the twenty-eight original members of the Royal Academy who were nominated by George III in 1768. He was elected the first Professor of Architecture to the Academy, and delivered the first of a series of six lectures in that capacity on Monday 8th October 1770. The sixth was illustrated by about forty drawings of buildings, ancient and modern, including original designs for a ‘Bridge of Magnificence,’ which attracted much attention. He continued these lectures with alterations and additions annually till his death. They were never published, but the manuscript is in the library of the Royal Institute of British Architects. The illustrations were sold with his other drawings after his death.

In February 1769, Sandby competed for the design of the Royal Exchange in Dublin, and obtained the third premium. His only architectural work in London was the Freemasons' Hall in Queen Street, Lincoln's Inn Fields, which was opened with great ceremony on 23rd May 1776, when the title of ‘Grand Architect’ was conferred upon Sandby. The building was partially destroyed by fire on 3rd May 1883, but was later restored. Sandby designed a carved oak altar-screen for St. George's Chapel, Windsor, now replaced by a reredos, and a stone bridge over the Thames at Staines, opened in 1796, but removed a few years afterwards on account of its insecurity. He built several houses in the neighbourhood of Windsor, including St. Leonard's Hill at Clewer for the Duchess of Gloucester, Holly Grove (now Forest Lodge) in the Great Park for Colonel Deacon and Ascot Place in Cranbourne for Andrew Lindegren, a Swedish ironmaster. Designs exist for many of his other architectural works which cannot now be identified. In 1777, he was appointed, jointly with James Adam, Architect of His Majesty's Works and, in 1780, Master-Carpenter of the same in England. Sandby died at the Deputy Ranger's Lodge in Windsor Great Park on Monday 25th June 1798. He was buried in the churchyard of Old Windsor.

Sandby was twice married. The name of his first wife is stated to have been Schultz. His second wife was Elizabeth Venables (1733–1782), to whom he was married on 26th April 1753. She had a dowry of £2,000 and bore him ten children, six of whom - five daughters and one son - survived him. It is to be observed that, in his will and in some simple verses addressed to his daughters after their mother's death, he names four only, Harriott, Charlotte, Maria and Ann, omitting his eldest girl, Elizabeth, who was twice married, and is said to have died about 1809. His daughter Harriott married (1786) Thomas Paul Sandby, the second son of his brother Paul, and kept house for her father after her mother's death. Eight of her thirteen children were born at the Deputy Ranger's Lodge. 

Though he was self-educated as an architect and left few buildings by which his capacity can be tested, the Hall of the Freemasons showed no ordinary taste (until replaced in 1932 due to structural problems caused by a much earlier fire), while of his skill as an engineer and landscape-gardener, Windsor Great Park and Virginia Water are a permanent record. He was an excellent and versatile draughtsman and so skilful in the use of watercolour that his name deserves to be associated with that of his brother, Paul, in the history of that branch of art.