Gates and Manafort were indicted by Mueller in October on a series of money laundering and fraud charges related to their Ukraine work.
District Court Judge Amy Berman Jackson also ordered van der Zwaan to pay a $20,000 fine.
The description of "Person A" in court records matches Konstantin Kilimnik, who worked for Manafort's consulting firm in Ukraine. John Dowd, Trump's former attorney, called for Mueller's probe to be shut down.
Jackson said she did not know if van der Zwaan was motivated to join Manafort and Gates for excitement, the money, or was engaged in a deeper "coverup", but that in lying "he put his own interests ahead of the interests of justice" in an investigation of national and worldwide importance into whether the US democratic process was corrupted.
The memo, dated August 2, 2017, and signed by Deputy Attorney General Rod Rosenstein, supplements a May 2017 appointment order directing Mueller to investigate possible coordination between Russian Federation and the Trump campaign, as well as "any matters that arose or may arise directly" from his probe.
Gates has since pleaded guilty in a deal with Mueller on charges of conspiring against the US and of making false statements to the federal government. He helped put together a dubious report clearing Yanukovych for jailing his political rival in 2011, then lied to Mueller's investigators about conversations he later had about the report with Gates and a person only identified as "Person A" by the special counsel's team. They also noted that Rosenstein has said publicly that he is supervising the investigation closely and that he does not believe Mueller has exceeded his authority.
They believe having van der Zwaan spend time in prison would serve as a deterrent. Mr Gates has admitted conspiracy and lying to investigators in a plea deal. In the process of looking into Manafort and Gates's ties to the Kremlin, Mueller's team started investigating the Skadden Arps report.
Van der Zwaan has no known ties to the Trump campaign but court documents say he and Gates held discussions with a business associate and former Russian intelligence officer during the final months of the 2016 campaign. "I apologize to my wife and my family", said van der Zwaan as he awaited sentencing. Manafort has pleaded not guilty and denied any wrongdoing related to Russian election interference.