A Tasmanian man charged with raping a two-year-girl and producing child exploitation material has changed his plea to guilty.

The 24-year-old man had pleaded not guilty in December and changed his plea in the Supreme Court in Hobart this morning.

The prosecution told the court the man raped the daughter of a woman he was in a relationship with at the woman's North Hobart home in October.

The court heard the man filmed the rape on a mobile phone and filmed another assault on the girl in a public toilet in central Hobart on the same day.

The owner of the phone later discovered the material.

Prosecutors said the man decided to change his plea after police showed him evidence in December.

He also pleaded guilty to the armed robbery of a New Town video store in September.

In a victim impact statement to the court, the girl's mother said she expected to have endless nightmares for the rest of her life.

He will be sentenced at the end of the month.