The Royal Observatory, Edinburgh (ROE) is an astronomical institution located on Blackford Hill in Edinburgh. The site is owned by the Science and Technology Facilities Council (STFC). The ROE comprises the UK Astronomy Technology Centre (UK ATC) of STFC, the Institute for Astronomy of the School of Physics and Astronomy of the University of Edinburgh, and the ROE Visitor Centre.

The observatory carries out astronomical research and university teaching; design, project management, and construction of instruments and telescopes for astronomical observatories; and teacher training in astronomy and outreach to the public. The ROE Library includes the Crawford Collection of books and manuscripts gifted in 1888 by the 26th Earl of Crawford. Before it moved to the present site in 1896, the Royal Observatory was located on Calton Hill, close to the centre of Edinburgh, at what is now known as the City Observatory.

The University of Edinburgh in 1785 and by Royal Warrant of George III created the Regius Chair of Astronomy and appointed Robert Blair first Regius Professor of Astronomy. After his death in 1828 the position remained vacant until 1834. In 1811 private citizens had founded the Astronomical Institution of Edinburgh with John Playfair – professor of natural philosophy – as its president. The Institution acquired grounds on Calton Hill to build an observatory, which was designed by John's nephew William Henry Playfair; it remains to this day as the Playfair building of the City Observatory.

During his visit of Edinburgh in 1822, George IV bestowed upon the observatory the title of "Royal Observatory of King George the Fourth". In 1834 – with Government funding – the instrumentation of the observatory was completed. This cleared the way to uniting the observatory with the Regius Chair, and Thomas Henderson was appointed the first Astronomer Royal for Scotland and second Regius Professor of Astronomy. The main instruments of the new observatory were a 6.4-inch (16 cm) transit telescope and a 3.5-inch (9 cm) azimuth circle.

In 1852 Charles Piazzi Smyth – second Astronomer Royal for Scotland – came up with the idea of building astronomical observatories on high mountains with good weather. He travelled to Tenerife a few years later for site testing. Nothing came of it until about 100 years later, when this mode of operation became common practice the world over. A time service was established in 1858. Timings of star transits were used to keep the observatory clock accurate. The clock was wired up to control the drop of a time ball on Nelson's Monument. This is visible from the port of Leith, thus providing accurate time for shipping. Another wire led to a time gun on Edinburgh Castle.

Chronic underfunding by the Government eventually led to Smyth's resignation in 1888. The Government then intended to close the Royal Observatory and to abolish the post of Astronomer Royal for Scotland.

When the Earl of Crawford learned of the plans to close the Royal Observatory, he offered to give the instruments of his own Dunecht observatory and his unique astronomical library to the nation on condition that the Government build and maintain a new Royal Observatory to replace the one on Calton Hill. Ralph Copeland was appointed third Astronomer Royal for Scotland and oversaw the move of the two observatories from Dunecht and Calton Hill to Blackford Hill. The new site was opened in April 1896.

The instruments to move into the domes were a 15-inch (38 cm) refractor (East Dome) and a 24-inch (0.6 m) reflector (West Dome). An 8.5-inch (22 cm) transit circle was housed in a separate building further west. The time service continued to control the time ball on Calton Hill and the time gun on Edinburgh Castle by telegraph wire. It also controlled a time gun in Dundee and a clock at Rosyth dockyard. In the 1910s and 1920s research at the ROE led to more accurate pendulum clocks, which remained in service until they had to give way to quartz clocks in the 1960s.