After qualifying for his Sports Car Club of America national license in 1984, he won the Northeast Division title in Formula Ford.

He earned his first ARS victory, at Pocono, as his father won the CART race at the same meeting, after his brother, Michael had started from pole, giving the Andretti family a "clean sweep".

He would revisit the top step of the podium in the series finale, in the race around Tamiami Park, Miami, snatching second place in the championship away from Tommy Byrne in the process.

After failing to qualify for the Indianapolis 500, he make his race debut with TEAMKAR International in their Lola-Cosworth T89/00 in the Miller Genuine Draft 200 on the Milwaukee Mile, only to suffer mechanical problems and not finish.

[3][8][9] In May 1991, Andretti qualified 11th for the Indianapolis 500, coupled with an outstanding performance before mechanical problems earned him the Indy 500 Rookie of the Year title.

However, he became yet another victim of the infamous Andretti Curse at the famed race track when on lap 109, a right rear wheel came loose off his car at turn 2 and he crashed violently head-on into the wall, smashing both his legs.

Andretti's fast run came at the conclusion of two days of testing where he consistently posted laps in the 230 mph range.

In 1994, Jeff did a one-off race with Euromotorsports, finishing 17th in the Slick 50 200, held at Phoenix Raceway, 21 laps adrift.

In May 1994, Jeff switched to Hemelgarn Racing, but his bid for a fourth consecutive start failed due to a blown Buick engine.