Court documents released by the ministry said that Mohammed Sleiman, from Israeli-annexed east Jerusalem, admitted to five counts of attempted murder in a plea bargain.
In March, Sleiman ploughed into a group of Israeli border policewomen as they crossed a busy road outside their base on the line separating west and east Jerusalem, wounding four of them.
He then hit a civilian cyclist, the court transcript said.
"Immediately afterwards, the accused stopped his vehicle, and got out, carrying an axe," it said.
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The prosecution said the attack was premeditated.
"He had decided in his heart to carry out a terrorist attack by murdering Jews," the transcript read.
In addition to the jail term, Sleiman was ordered to pay compensation totalling 260,00 shekels (USD 68,420).
The March 6 incident mirrored a spate of attacks in Jerusalem in October and November last year, where Palestinians drove into groups of pedestrians, killing several people.