The slot value for the pick was $6,821,800.
Miami has aggressively pursued its picks from each of the first 10 rounds.
With Kolek, negotiations advanced quickly. The deal was basically in place a few days ago, but it has been pending completion of physicals.
The Marlins have not officially announced the signing.
Miami has also come to a deal with catcher Blake Anderson, the 36th overall pick. His deal is for $1.17 million.
Shortstop Justin Twine, the 43rd overall pick, was taken in the second round, and he will receive a bonus of $1.316 million. Second baseman Brian Anderson, a third-round selection, is signing for $600,000.
Kolek is Miami's prize pick.
Raised on a 10,000-acre ranch in Shepherd, Texas, Kolek has a fastball that has been clocked as high as 102 mph, the highest reading ever by a high school player.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter