The court said Mussa Ajlouni, 25, a resident of the Old City, pleaded guilty in a plea bargain to two counts of attempted murder over the December 26 attack on the officers, near his home.
Video of the incident shows the terrorist approaching the two border policemen from behind and violently attacking them.
Police at the time described the injuries as light, but the charge sheet said one of the officers suffered damage to tendons and nerves in his hand and required further treatment. The other victim had a cut to his neck.
Ajlouni was arrested in early January on suspicion of carrying out the stabbing attack at a security checkpoint near the Lions Gate of the Old City.
Under interrogation Ajlouni admitted responsibility for the attack, and told how he prepared and hid the large knife in advance.
The stabbing came at a time of frequent Arab riots in eastern Jerusalem, as well as a series of deadly "lone wolf" attacks on Israeli civilians.
A more intense round of terror erupted at the start of October 2015; 12 Israelis have so far been killed and over 160 wounded.
AFP contributed to this report.