The hosts have already clinched the series, the third Test in Melbourne having finished in a draw on Tuesday after they won the first two matches.
And, with the Sydney wicket traditionally helpful to slow bowlers, Agar will join off-spinner Nathan Lyon in the squad and give the Aussies an extra option.
The 21-year-old is best known for his exploits in the first Ashes Test at Trent Bridge last year, when he scored 98 on his debut, batting at number 11.
However, he was not as successful with the ball and has not played for Australia since the second Test of that series.
Australia captain Steve Smith said: ???He’s bowling very well at the moment, he’s a good addition to the squad.
???We’ll see how the wicket is in Sydney when we get there and we’ll go from there.
???We’re not too sure what it will be like. Last year it had a bit of grass on it and previously it’s been quite a spin friendly wicket.
???I think it’s more of a see how the wicket is and, if he’s needed, then he can play.”
There were no other changes to the squad and 35-year-old seamer Ryan Harris says he will be fit for the Sydney match, which gets underway on 6 January.
Having had knee surgery, Harris is carefully managed and was rested for the second Test, but he was named man-of-the-match in Melbourne after making 74 in the first innings and taking six wickets in the match.
“I’m playing in Sydney, if I get picked,” he said.