https://en.wikipedia.org/wiki/List_of_districts_of_Tamil_Nadu#Pre-independence

Madras Presidency           -----15Aug1947(26 districts)

Madras Province              -----15Aug1947-26Jan.1950

Madras State                    -----26Jan.1950-1Nov.1956

Tamil Nadu State             -----1Nov.1956(13 districts)-now(38 districts)

The Tamil speaking region Kanyakumari was merged to Madras state which was earlier a part of Travancore-Cochin. Madras state was formed on 1 November 1956, with 13 southern districts of Madras Presidency.

They are: Chingleput, Coimbatore, Kanyakumari, Madras, Madurai, Nilgiris, North Arcot, 

                Ramanathapuram, Salem, South Arcot, Thanjavur, Tiruchirappalli and Tirunelveli.

List of districts of Tamil Nadu

The Indian state of Tamil Nadu has 38 districts after several splits of the original 13 districts at the formation of the state on 1 November 1956. The states are further divided into taluks and smaller administrative units.

The Madras Presidency in 1913

Pre-independence See also: Administrative divisions of Madras Presidency

At the time of Independence, Madras Presidency in India was made up of 26 districts, of which 12 districts were found in the present-day Tamil Nadu, namely, Chingleput, Coimbatore, Nilgiris, North Arcot, Madras, Madura, Ramnad, Salem, South Arcot, Tanjore, Tinnevely, and Trichinopoly.

1.Chingleput

2.Coimbatore

3.Nilgiris

4.North Arcot

5.Madras

6.Madura

7.Ramnad

8.Salem

9.South Arcot

10.Tanjore

11.Tinnevely

12.Trichinopoly.

1947 – 1950 After Indian Independence, the Madras Presidency under British rule became the Madras Province on 15 August 1947. After Indian independence in 1947, the Pudukkottai Princely State was amalgamated with Indian Union on 4 March 1948 and became a division in Trichinopoly district. The new Constitution of India, which came into force on 26 January 1950, made India a sovereign democratic republic. The new republic was also declared to be a "Union of States".[1] According to this act, on 26 January 1950, Madras Province was formed as Madras State by the Government of India.

1950 – 1956

Map of Southern India (1953–1956) before the States Reorganisation Act of 1956 with Madras State in yellow

At the time of formation of Madras State in 1950, it included the whole of present-day Tamil Nadu, Coastal Andhra, Rayalaseema, the Malabar region of North Kerala, Bellary and South Canara. Coastal Andhra and Rayalaseema were separated to form Andhra State in 1953, while South Canara and Bellary districts were merged with Mysore State to form Karnataka state, and Malabar District with the State of Travancore-Cochin to form Kerala in 1956.

Madras state, 1950= present TN+ Present A.P.(=the earlier Andhra State formed in 1953)

                                                                            +

                                                   South Canara dt. + Bellary Dt.(merged with Mysore State to form Karnataka in 1956)

                                                                            +

                                                   Malabar District (merged with the State of Travancore-Cochin to form Kerala in 1956)