The cars feature Speedgear, an electronically-controlled continuously variable automatic transmission (ECVT) which provides a six or seven-speed sequential manual gearbox.
Punto Sporting, a 3dr model priced £11,995, has seven forward speeds and Punto ELX, a 5dr version at £10,995, has six. Both have 1.2-litre 16v engines.
Fiat predicts that the two derivatives will account for about 7% of UK Punto sales - an increase on last year's segment average for automatic transmission vehicles.
In the first four months of this year, more than 18,000 Puntos were sold in the UK. Its best year was 1998 with sales of more than 52,000 units.
Fiat Auto claims the Punto is the only vehicle in its class to offer ECVT transmission that can also be used as a six or seven-speed manual gearbox.
The Speedgear system offers a choice between a full automatic and a manual shift with sequential engagement - two gearboxes in one with three operating systems.