Baker was born in the parish of Alphington, near Exeter, Devon, as is recorded on his mural monument in Dunchideock Church.
Madras period
Baker was the first President of Madras when the Presidency of Fort St George was created in the year 1652. He served as President from 1652 to 1655. In 1652-53, caste conflicts arose between "left-hand" and "right-hand castes" which was settled by the English, who reserved the eastern half of the Indian quarter of the city for the "left-hand" castes and the western half of the quarter for the "right-hand" castes. During this period the area around Madras was in great turmoil due to the rebellion of Mir Jumla against his overlord in Golconda. During this time Bala Rao, the chief of Poonamallee, raised the customs duties on English goods thereby causing a drastic increase in prices. Madras was besieged by Bala Rao and his colleague, Tupaki Krishnappa Naick. This blockade and the economic boycott of English trade by Bala Rao forced the English to reduce Fort St George from a Presidency to an Agency at the termination of Baker's term of office.
Dismissal
Private trade was eventually allowed while holding Presidency positions but had at first been frowned upon; both Aaron Baker and Sir Edward Winter were ultimately dismissed for engaging in it.
Retirement in England
Baker retired to Bowhay in the parish of Exminster, Devon, England, with the fortunes he earned. In 1669 he rebuilt the north chancel aisle of St. Michael's church in Dunchideock, near Exminster, where is a monument to his memory.
Marriages
Baker married twice:
Firstly to a certain Elizabeth, who died in childbirth at sea when on her way to join her husband in Madras, and has the distinction of having the oldest English tombstone in India.
Secondly on 25 July 1672, in the parish church of Dunchideock, Devon, "Mr. Aaron Baker of Exminster" married "Mrs Mary Rowe of the parish of Ayston".
A mural monument to Aaron Baker survives in St Michael's Church, Dunchideock, situated on the north wall of the north aisle chapel. It is inscribed in Latin as follows:
Above are shown the arms of Baker: Argent, on a saltire engrailed sable five escallops of the first on a chief of the second a lion passant of the first; impaling the arms of his two wives: in chief: Or, a fess between three Catherine wheels sable ; in base: Gules, on a chevron argent a lion rampant sable. Above is the crest of Baker: A man's dexter arm embowed argent garnished or grasping in the hand an arrow point downward of the last.