He said he reached for his revolver and shot Angelotti in the chest and seriously wounded another thief in the neck.
A third fled but was later arrested by police.
"I was afraid and I fired," Mr Polimadei told police. "I didn't understand a thing. I felt in danger with their pistols pointed at me. I shot several times."
Angelotti was accused of murdering a jeweller in Florence in 1992 and sentenced in 1998 but released from prison a year later.
He had also been arrested on charges of drug trafficking, loan sharking and illegal gambling.
Angelotti, whose nickname was 'Caprotto', was best known as the gang member who betrayed Enrico De Pedis, a leader of the Magliana, gunned down by rival gangsters in 1990.
Rome Mayor Gianni Alemanno described the murder of Angelotti as "a great act of courage" and offered his support to the jewellers.