A method programs a memory cell comprising: an initial phase in which a continuous voltage is applied to a drain terminal of said memory cell and a suitable programming voltage signal is applied to a gate terminal thereof; a regulation phase in which a constant voltage value is applied to said gate terminal and a voltage value of said drain terminal is regulated so as to be maintained at a fixed value until a threshold voltage value of said memory cell is set at a desired threshold voltage level; and a disable phase that stops said programming and is triggered as soon as a programming current value of said memory cell goes below a reference current value, said reference current value corresponding to the attainment by the threshold voltage value of said memory cell of the desired threshold voltage value. A programming circuit is suitable for implementing this method.