The deal is worth $2.3 million, according to a source familiar with the negotiations.
Cecchini will report to Port St. Lucie for mini-camp starting Monday and then join Rookie-level Kingsport of the Appalachian League when its season opens on June 19.
The 18-year-old from Lake Charles, La., finished his senior season with a .413 average, seven home runs, 32 RBIs and 31 stolen bases.
Coming from a baseball family, Cecchini's father, Glenn, coached him at Barbe High School and his brother, Garon, was a fourth-round pick by the Red Sox in 2010.
"This is who I wanted to be drafted by all along," said Cecchini, the brother of Red Sox third-base prospect. "There's not a better place to play baseball than New York."
Mets scouting director Tommy Tanous described him as an "offensive shortstop" who "doesn't give away much defensively," which jives with most reports of Cecchini's abilities. The Mets view him as another high-ceiling bat to complement Nimmo, whose first-round selection last year represented a paradigm shift within the organization.
Quinn Roberts is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.