NEW YORK — Stephen Strasburg and the Washington Nationals agreed to a contract just before Monday’s midnight deadline.

The San Diego State right-hander, being advised by Scott Boras, was selected first by the last-place Nationals in June and was seeking to set the mark for the most money guaranteed to a drafted player. That’s been held since 2001 by pitcher Mark Prior, who received a $10.5 million, five-year contract after he was selected with the second pick, behind Joe Mauer.

Strasburg was among 16 of 32 first-round picks without announced agreements heading into the final day, and most of them reached deals.

Boras represented six of the unsigned first-round picks, including the second, third, ninth, 13th and 30th selections.

In addition to Strasburg, he negotiated agreements for Dustin Ackley, a North Carolina center fielder taken by No. 2 Seattle; Donavan Tate, a center fielder from Cartersville High School in Georgia selected No. 3 by San Diego; and Grant Green, a Southern Cal shortstop drafted No. 13 by Oakland.

He also was thought to have negotiated a deal for Jacob Turner, a right-hander from Westminster Christian Academy in Missouri taken by No. 9 Detroit.

San Diego announced an agreement with Tate less than two hours before the deadline, a deal worth about $6.25 million. He had planned to play football and baseball at North Carolina.

Tampa Bay said it didn’t think it would agree with another Boras client, LeVon Washington, a second baseman from Buchholz High School in Florida taken by Tampa Bay with the 30th pick.

‘‘We are disappointed that LeVon has chosen not to sign with the Rays. We offered him a bonus consistent with late first-round picks,’’ Rays executive vice president of baseball operations Andrew Friedman. ‘‘Immediately following the draft, he seemed eager to sign but it has not materialized. We wish LeVon great success with his baseball career.’’