Jani was born in Rorschach, Switzerland. His mother is Swiss and his father Indian. He started racing karts in 1996 moving into single seaters in 2000 in Formula List Junior. He won the Swiss Championship with 8 wins and 4 seconds from 12 races.
He joined the Formula Renault Eurocup and Italian series in 2001.
Staying in Formula Renault for 2002 he once again racing in both series though only part of the Italian season. In 2003 he joined Jenzer in the Formula Renault V6 Eurocup.
He stayed in V6 Eurocup for 2004, driving for the DAMS team this time, whilst also one race for DAMS' FIA GT Championship team.
He was linked to an F1 seat with the Sauber team in 2004. However in 2005 he raced in GP2 with Racing Engineering alongside Borja Garcia, who he generally outperformed. He won two races, at the Hungaroring and at Monza. He also managed to lead most of the Nürburgring race in a clearly slower car with some effective defensive driving.
In 2006 he was signed as the third driver for F1 team SCUDERIA TORRO ROSSO. In GP2 he replaced Nicolas Lapierre, who was injured, in the Silverstone and Magny-Cours races for Arden. By doing this he also secured his place in the record books, being the only person to ever drive in both GP2 and F1 on the same day.
He then raced in the new A1 Grand Prix series, representing his home nation with A1 Team Switzerland. In the inaugural season of A1GP, the team earned the silver medal for second place, with Jani consistently finishing on the podium, including a win at the Dubai Autodrome during the Sprint Race of the 2005-06 A1 Grand Prix of Nations, United Arab Emirates.
After missing the first two rounds of the 2006-07 season in favour Sébastien Buemi, Jani would win another Sprint Race, during the 2006-07 A1 Grand Prix of Nations, Malaysia.
For 2007 he is racing in the Champ Car World Series for Red Bull PKV Racing.