Cliff Sims is bringing the suit against Trump "in his official capacity as President" and is seeking an injunction against the agreements, reports CNN.
The White House is yet to comment on the lawsuit filed on Monday.
Sims's book, "Team of Vipers: My 500 Extraordinary Days in the Trump White House", released in January, is his candid account of a chaotic White House.
In response, Trump said following the book's release that he hardly knew Sims and it was "yet another boring book based on made-up stories and fiction".
"The US government is intentionally and unconstitutionally engaging in a subterfuge effort to use a private entity, Donald Trump for President, Inc., to do its bidding to silence Sims when it is really the intense powers of the Presidency coming down upon a sole individual," Mark Zaid, Sims's attorney, said in the lawsuit.