Anders Petersen was born in Bjæverskov as the youngest of four children of farmer Peter Nicolaisen and wife Marie Nilsdatter Bech.
He grew up with his family in the residence of the deacon of Bjæverskov, where his parents worked for the unmarried deacon. Since rural deacons were often school teachers as well, this may partly explain why he later became a teacher.
In 1842 he was confirmed as first in his class.
The deacon who had employed his parents died in May the same year, two months later at the age of 14 Anders Petersen started as an apprentice as a weaver in nearby Slimminge.
In May 1845 Anders Petersen had completed his apprenticeship. During the following years he worked as a weaver in various nearby villages except for November 1846 where he lived in Copenhagen. In November 1849 he returned to his parents in Bjæverskov. Since his father was over 60 and working as a day labourer he may have moved back to support his parents.
In 1850 he volunteered for the army and soon became a non-commissioned officer in the artillery.
The following year his father died, six years later his mother died.
In 1852 he entered Jonstrup Seminarium on a stipend from Count Brockenhus Schack of Giesegaard to become a teacher and in 1855 he graduated.
On 12 June 1857 he married Olivia Anine Vilhemine Ømann in Garrison Church, Copenhagen.
From 1857 to 1886 he was a school teacher in Vallø by.
While living there he and his wife had four daughters, Petrine Marie Isabella Petersen (19 February 1858), Agnes Theodora Elna Petersen (22 April 1860), Olga Dagmar Nicoline Petersen (14 June 1862) and Thora Astrid Vilhelmine Petersen (19 September 1873).
On 25 June 1879 he was a Dannebrogsmand i.e. he had been awarded the Cross of Honour of the Order of the Dannebrog (Dannebrogsmændenes Hæderstegn).
In 1886 when his daughter Agnes married a teacher he was her best man as teacher and church singer.
In 1890 he had been awarded the silver medal of merit (fortjenstmedalje) and lived in Køge as a retired teacher with his wife and two unmarried daughters of whom the oldest (Petrine) was herself a teacher.
In 1891 he moved with his wife from Køge to Wesselsgade 13-2, Copenhagen as a retired teacher.
In 1901 two of his daughters had died.
After he retired Anders Petersen remained an active author.
Anders Petersen has a posthumous entry in the 1914 issue of Kraks Blå Bog as author and teacher.
The Danish National Archives has preserved some of his mail correspondence.
In 1991 a group of Danish historians led by J. Ingemann Pedersen raised the funds to reprint Anders Petersens book Sjællands Stifts Degnehistorie, which is very useful to genealogists but which had become very rare.