He denies three remaining charges, two allegations of attempting to pervert the course of justice and one of understating election expenses.
At the High Court in Edinburgh, Lady Cosgrove acquitted him after a withdrawal of the charge by Advocate Depute Duncan Menzies.
The move came as the Crown case was closed on the 29th day of the trial.
The MP's co-accused, Mumtaz Hussain, 41, from Lesmahagow, Lanarkshire, denies one charge of attempting to pervert the course of justice.
Mr Sarwar, 46, of Pollokshields, Glasgow, became Britain's first Muslim MP when he was elected for Glasgow Govan in May 1997.
Weeks afterwards the News of the World claimed he had paid an election rival a pounds 5,000 cash "bung".
The charge Mr Sarwar was cleared of had accused him of responsibility for adding to the electoral register the names of people who were not qualified to vote in the constituency. The Crown alleged that several Asian individuals had used late application forms to register, at Mr Sarwar's bidding.
It also emerged that he had been forced to give a police interview on the day he had planned to make his first speech in Parliament on December 5 1997.
An investigating officer admitted that fact during questioning and added that police had been unhappy with 36 applications from late voters.
The trial was adjourned until tomorrow.Reuse content