Sidhu, an MP with the Hindu nationalist Bhartiya Janata Party (BJP), was found guilty of "culpable homicide not amounting to murder" - a charge roughly equivalent to manslaughter - for the 1988 incident.
Sidhu's sentence is to be announced next Wednesday. Lawyers said he faces up to 10 years in jail, but he can lodge an appeal with the Supreme Court.
"I have asked for permission to resign. I am sending my resignation now," 43-year-old Sidhu told reporters on Friday.
The police complaint against Sidhu said the former cricketer and his accomplice dragged the victim out of his car and showered him with punches and blows after a road accident.
He had previously been acquitted in the case in 1999 by a lower court.
Sidhu played 51 Test matches and 136 one-day internationals between 1983 and 1999 and has been a popular cricket commentator on television channels.
He courted controversy in 1996 by deserting the Indian team during a tour of England after a spat with captain Mohammad Azharuddin.
The former cricketer's use of proverbs and cliches on TV shows has become so popular that his one-liners are known as 'Sidhuisms'.
The verdict comes just days after India's coal minister, Shibu Soren, was found guilty of conspiracy in the murder and abduction of a former aide who was allegedly blackmailing the minister in a bribery scandal.
Soren -- the first cabinet minister to be found guilty in a murder case -- could get the death penalty when the court announces the sentence Tuesday.
A day after Soren's conviction, the BJP took the government to task for giving ministerial positions to politicians facing police charges.