Mr Lee was not present at the preliminary hearing, but his lawyer denied all charges on his behalf, reports The BBC.
The case is linked to a massive scandal that led to the impeachment of South Korea’s President Park Geun-hye.
Four other Samsung executives who are also facing trial have also denied wrongdoing.
The trial is expected to go on for several months.
Mr Lee, also known as Jay Y Lee, is currently vice-chairman of Samsung Electronics. But since his father, Lee Kun-hee, suffered a heart attack in 2014, he is considered de facto boss of the entire Samsung Group conglomerate.
He is accused of giving donations worth 41bn won ($36m;£29m) non-profit foundations operated by Choi Soon-sil, a friend of Ms Park.
Prosecutors have alleged this was done to win government support for a big restructuring of Samsung that would help a smooth leadership transition in favour of Mr Lee.
In a December parliamentary hearing, Samsung admitted giving a total of 20.4bn won to two foundations, but denied seeking favours in return.
Mr Lee also confirmed the firm gave a horse and money to help the equestrian career of Ms Choi’s daughter, Chung Yoo-ra, something he said he now regrets.