Low Taek Jho, known as Jho Low, allegedly transferred more than $21m (£16m) to musician Prakazrel Michel to make the payments.
Mr Michel has appeared in court and pleaded not guilty to the charges.
Mr Low, whose whereabouts are unknown, also denies any involvement.
Both men have been charged with one count of conspiracy to defraud the US government. Mr Michel has been charged with one count of a scheme to conceal material facts and two counts of making a false entry in a record.
Mr Low's payments were allegedly made during June and November 2012.
Mr Michel reportedly paid $865,000 to around 20 people so that they could make donations in their names to a presidential joint fundraising committee.
He also allegedly made more than $1m in donations to a political committee in his name.
Court documents claim that they aimed to "gain access" to one of the presidential candidates, named as "Candidate A".
Mr Michel was known to be a strong supporter of Barack Obama, who was re-elected president in that year.
Mr Michel's attorney Barry Pollack said: "Mr. Michel is extremely disappointed that so many years after the fact the government would bring charges related to the 2012 campaign contributions. Mr Michel is innocent of these charges and looks forward to having the case heard by a jury."
A spokesperson for Mr Low said: "The allegations against Mr Low have no basis in fact. Mr Low has never made any campaign contributions directly or indirectly in the US and he unequivocally denies any involvement in or knowledge of the alleged activities."
Mr Low is facing separate criminal charges in the US in connection with a financial scandal in Malaysia. He is accused of being involved in the alleged theft of around $4.5bn from Malaysia's investment fund 1MDB.