The Melbourne City Centre does not have current official boundaries, but rather is commonly understood to be the Hoddle Grid plus the parallel  streets immediately to the north, including the Queen Victoria Market, and the area between Flinders Street and the river.
There are a number of officially demarcated areas which are similar, but all differ slightly.
Some that are larger still use the term 'Melbourne', which leads to some confusion.

The boundaries of the Australian Bureau of Statistics (ABS) Statistical Area Level 2 'Melbourne' is a good representation of the commonly understood area of 'the CBD'; it includes the Hoddle Grid, plus the area of parallel streets just to the north up to Victoria Street including the Queen Victoria Market, but not the Flagstaff Gardens or the streets to the west of it, and the area between Flinders Street and the Yarra river west of Swanston Street.
A map can be found here.
This is not to be confused with the State Suburb level area, also called Melbourne, which is a larger area.

The area of the postcode 3000 is very similar, but also includes the area to the east of Flinders Street Station, and a leg up northern Elizabeth Street.
A map of this can be found here and here.

The locality (suburb) of Melbourne is an official area, but is larger; it is the area of postcode 3000 combined with the area of postcode 3004 (an area to the south of the central city, including the Domain and Botanic Gardens parklands, and the east side of St Kilda Road) and both of these postcodes are known as Melbourne.

The term Central Business District, or 'CBD', was first used in the Report on a planning scheme for the central business area of the City of Melbourne by town planner E.F. Borrie, which was commissioned by the City of Melbourne, and published in 1964.
The maps used in the report show the CBD as just the Hoddle Grid, plus the parallel streets immediately to the north, and the area between Flinders Street and the river, very similar to the ABS area.

Since 1999, the Melbourne Planning Scheme has included a 'Capital City Zone' which is a much larger area, including the former CBD, minus the RMIT area, but including Southern Cross Station, much of Southbank down a line along the Westgate Freeway, Kingsway, down to Coventry Street, South Melbourne, and the north wharf area and the South Wharf area.
A map of the CCZ can be found here.
The area described as 'the central city' in Clause 21.08 of the Melbourne Planning Scheme is similar, but also includes the Docklands.

There are several adjoining areas that have important functions that are sometimes included within the idea of 'the CBD' or the central city, such as Parliament House and the Treasury buildings on Spring Street, which are officially in East Melbourne, and Southern Cross railway station on Spencer Street, which is officially in Docklands.
Other areas have in the last 30 years years become heavily developed with apartments, office buildings and important functions similar to the CBD, and are sometimes incorporated, such as the Docklands (with Docklands Stadium) to the west, and Southbank and South Wharf on the other side of the Yarra River.

Despite the area being described as the city centre, it is neither the geographic or demographic centre of Melbourne; due to urban sprawl to the south east the geographic centre is in the southeastern suburbs (in 2002 is was located at Bourne Street, Glen Iris).
The Melbourne City Centre does not have current official boundaries, but rather is commonly understood to be the Hoddle Grid plus the parallel  streets immediately to the north, including the Queen Victoria Market, and the area between Flinders Street and the river. There are a number of officially demarcated areas which are similar, but all differ slightly. Some that are larger still use the term 'Melbourne', which leads to some confusion.
The boundaries of the Australian Bureau of Statistics (ABS) Statistical Area Level 2 'Melbourne' is a good representation of the commonly understood area of 'the CBD'; it includes the Hoddle Grid, plus the area of parallel streets just to the north up to Victoria Street including the Queen Victoria Market, but not the Flagstaff Gardens or the streets to the west of it, and the area between Flinders Street and the Yarra river west of Swanston Street. A map can be found here. This is not to be confused with the State Suburb level area, also called Melbourne, which is a larger area.
The area of the postcode 3000 is very similar, but also includes the area to the east of Flinders Street Station, and a leg up northern Elizabeth Street. A map of this can be found here and here.
The locality (suburb) of Melbourne is an official area, but is larger; it is the area of postcode 3000 combined with the area of postcode 3004 (an area to the south of the central city, including the Domain and Botanic Gardens parklands, and the east side of St Kilda Road) and both of these postcodes are known as Melbourne.
The term Central Business District, or 'CBD', was first used in the Report on a planning scheme for the central business area of the City of Melbourne by town planner E.F. Borrie, which was commissioned by the City of Melbourne, and published in 1964. The maps used in the report show the CBD as just the Hoddle Grid, plus the parallel streets immediately to the north, and the area between Flinders Street and the river, very similar to the ABS area.
Since 1999, the Melbourne Planning Scheme has included a 'Capital City Zone' which is a much larger area, including the former CBD, minus the RMIT area, but including Southern Cross Station, much of Southbank down a line along the Westgate Freeway, Kingsway, down to Coventry Street, South Melbourne, and the north wharf area and the South Wharf area. A map of the CCZ can be found here. The area described as 'the central city' in Clause 21.08 of the Melbourne Planning Scheme is similar, but also includes the Docklands.
There are several adjoining areas that have important functions that are sometimes included within the idea of 'the CBD' or the central city, such as Parliament House and the Treasury buildings on Spring Street, which are officially in East Melbourne, and Southern Cross railway station on Spencer Street, which is officially in Docklands. Other areas have in the last 30 years years become heavily developed with apartments, office buildings and important functions similar to the CBD, and are sometimes incorporated, such as the Docklands (with Docklands Stadium) to the west, and Southbank and South Wharf on the other side of the Yarra River.
Despite the area being described as the city centre, it is neither the geographic or demographic centre of Melbourne; due to urban sprawl to the south east the geographic centre is in the southeastern suburbs (in 2002 is was located at Bourne Street, Glen Iris).
Melbourne city centre