Bryant's bonus will top Mark Appel's $6.35 million deal with the Astros. Byron Buxton received the highest bonus last year, $6 million, from the Twins.
With Friday's deadline to sign Bryant looming, he was one of four first-round picks yet to sign, joining Colin Moran (Marlins); Phil Bickford (Blue Jays); and Aaron Judge (Yankees).
Bryant's season ended in early June, and once the Cubs get the third baseman signed, he will report to their facility in Mesa, Ariz., to work out before being assigned to a Minor League team.
"We would need to get a feel for how rusty he is," Cubs general manager Jed Hoyer said Wednesday. "Once we get a feel for his conditioning, we'll figure out exactly what the right path is. Certainly, he'll start out at the very low levels [in the Minors]. We're hopeful he can move quickly through those."
Bryant, 20, was the second pick overall in the June Draft out of the University of San Diego. He was considered the best power college bat in the Draft after leading the nation in home runs (31), runs scored (80), walks and slugging percentage (.820). In 62 games, he batted .329 with 13 doubles and 62 RBIs. San Diego would bat him leadoff to avoid having teams pitch around him.
The third baseman received the Dick Howser trophy as the 2013 College Player of the Year.
Carrie Muskat is a reporter for MLB.com. She writes a blog, Muskat Ramblings, and you can follow her on Twitter @CarrieMuskat. This story was not subject to the approval of Major League Baseball or its clubs.