The station was opened on 19 September 1932 as the most northerly on the first section of the Piccadilly Line extension from Finsbury Park to Cockfosters. It was the terminus of the line until services were further extended to Oakwood on 13 March 1933. Its name was chosen after public deliberation: alternatives were "Arnos Park", "Bowes Road" and "Southgate".
Like the other stations Charles Holden designed for the extension, Arnos Grove was built in a modern European style using brick, glass and reinforced concrete and basic geometric shapes. A circular drum-like ticket hall of brick and glass panels rises from a low single-storey structure and is capped by a flat concrete roof. The design was inspired by the Stockholm City Library and Swedish architect Gunnar Asplund. A similar design was employed by Holden for the rebuilding of Chiswick Park on the District Line (also in 1932), although the drum there is supplemented with an adjacent brick tower. The centre of the ticket hall is occupied by a disused ticket office (a passimeter in London Underground parlance) which houses an exhibition on the station and the line. Like Holden's other stations on the extension, Arnos Grove is a Grade II listed building. The building is one of the 12 "Great Modern Buildings" profiled in The Guardian during October 2007, and was summarised by architectural critic Jonathan Glancey as "...truly what German art historians would describe as a gesamtkunstwerk, a total and entire work of art."
Three parallel train tracks pass through the station, with two double-sided platforms between the central track and the outer tracks. The edges of the platforms are labelled platform 1 and 2, and platform 3 and 4, in such a way that the two outer tracks are accessible from platforms 1 and 4, and the central track, usually used by trains that terminate and reverse at Arnos Grove station, is accessible from platforms 2 and 3. Platforms 1 and 2 are designated for trains to Cockfosters, platforms 3 and 4 for trains to Central London. When operational problems occur on the line, Arnos Grove station may act as a temporary terminus of a reduced service - either a shuttle service between Arnos Grove and Cockfosters or a truncated service from Central London. The station has a set of seven sidings to its south for stabling trains.
In 2005 the station underwent a refurbishment programme including improvements to signage, security and train information systems. Some of the original signs are in a 'petit-serif' adaptation of the London Undergroundtypeface, Johnston Sans. This type-face was designed by Charles Holden and Percy Delf Smith.
The station is part of the Arnos Grove group of stations, comprising all seven stations from Cockfosters to Turnpike Lane, and the management office for the group is in Arnos Grove station. Linked to the station by a lineside passageway is Ash House, which is a drivers' depot. Arnos Grove is often noted for its station cat (a rarity on the London Underground network), called Spooky, who now occupies the station car park after being evicted due to the introduction of UTS gates.