Sale, who was selected No. 13 overall in the 2010 First-Year Player Draft, became the highest-drafted player to agree to terms so far. The bonus is in line with MLB's bonus recommendation for the No. 13 slot.
He's expected to take his physical on Monday and sign the deal on Tuesday, according to the report.
The 6-foot-6, 185-pound pitcher impressed at Florida Gulf Coast this spring by posting an 11-0 record and a 2.01 ERA with 146 strikeouts in 103 inning as a junior.
He was scouted by the White Sox in the Cape Cod League, where he emerged as its top pitching prospect after going 4-2 with a 1.47 ERA and 57 strikeouts in 55 innings for Yarmouth-Dennis.
White Sox director of amateur scouting Doug Laumann said initially he was surprised about Sale falling to the club at the No. 13 pick in a conference call with reporters after they selected Sale on June 7.
"We've talked in previous conversations about the unpredictability of this Draft in particular, but yeah, I was surprised," said Laumann of the team's ability to select Sale. "We had this guy targeted to a certain degree, but a lot of projections had him going ahead of us. We are very happy to get him in this position."
The signing, however, didn't come as surprise, as Sale sounded confident that he'd sign with the White Sox after being drafted.
"I said it once and I'll say it again -- no one gets better working out a deal," Sale said in a teleconference. "I'm a baseball player and that's what I like to do, so the sooner the better."
Sale is expected to report to high Class A Winston-Salem, and could be promoted to Triple-A in July, with a chance to make it to the Majors as a reliever as early as August, according to the report. Sale, though, is targeted to be a starting pitcher long-term.
Rhett Bollinger is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.