Prosecutors say he gave 43bn Korean won ($38m; £30m) to President Park Guen-hye's friend for political favours.
Ms Park is suspected of colluding with Choi Soon-sil to get conglomerates to donate to Ms Choi's foundations.
Ms Park was arrested last week, after being impeached, and sent to a detention centre, although she has not yet been formally charged.
Mr Lee, who appeared in court in handcuffs, has denied the bribery allegations, saying Samsung was coerced into handing over the funds.
Another four Samsung executives have also appeared in court in connection with the scandal. They also deny the accusations.
Mr Lee's case is "one of the most deep-rooted and typical cases involving unhealthy relations between politicians and businessmen," said Special Prosecutor Park Young-Soo in his opening statement in Seoul's Central District Court.
Mr Lee, the 48-year-old vice-chairman of Samsung Electronics, has been the parent company Samsung Group's de facto head since his father Lee Kun-hee suffered a heart attack in 2014.
He was arrested in February.
On Friday, the chairman of the powerful Lotte conglomerate, Shin Dong-bin, was also being questioned by prosecutors in connection with the widening corruption probe.
They are investigating whether donations given by Lotte to foundations allegedly controlled by Ms Choi were bribes connected to the firm's bid for a lucrative duty-free business.
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