Mr Flynn is said to have misled officials about his call with Russia’s ambassador before his own appointment.
It is illegal for private citizens to conduct US diplomacy.
US reports said earlier the White House had been warned about the contacts last month and had been told Mr Flynn might be vulnerable to Russian blackmail.
The national security adviser is appointed by the president to serve as his or her chief adviser on international affairs and defence.
In his letter of resignation (PDF), Mr Flynn said he had “inadvertently briefed the vice-president-elect and others with incomplete information regarding my phone calls with the Russian ambassador” late last year.
The White House has appointed Lt Gen Joseph Keith Kellogg as his interim replacement.
Mr Flynn, a retired army lieutenant-general, initially denied having discussed sanctions with Ambassador Sergei Kislyak, and Vice-President Mike Pence publicly denied the allegations on his behalf.
But he came under further pressure on Monday when details of his phone call emerged in US media as well as reports the justice department had warned the White House about him misleading senior officials and being vulnerable to Russian blackmail.
According to the Washington Post, the message was delivered by then-Acting Attorney General Sally Yates, who was subsequently dismissed by President Trump for opposing his controversial travel ban.
The UK Defence Secretary, Sir Michael Fallon, said it was always best to be wary in dealing with Russia.
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