Boxberger, who was the 43rd overall pick out of the University of Southern California, received a bonus worth $857,000.
"We're excited," Reds scouting director Chris Buckley said. "We didn't want to say anything until we worked out all the terms. That's standard to get through the physicals. Everything is OK."
Both players and Reds general manager Walt Jocketty will meet with the media at 4 p.m. ET on Tuesday at Great American Ball Park.
Buckley said that Leake and Boxberger would be sent to the team's Spring Training complex in Sarasota. The Reds have a Gulf Coast and Class A Florida State League team there.
"Neither one of the guys have pitched in a game in a couple of months," Buckley said. "They have to get tuned up. I'm not sure they'll pitch before the season is over. They both pitched a lot of innings this year."
Leake was 16-1 with a 1.71 ERA, 24 walks and 162 strikeouts in 142 innings over 19 games this season. His 40 wins for the Sun Devils was tied for the most ever by a three-year player at ASU and is tied for third-most in school history.
The 21-year-old Leake was named the Pac-10 Pitcher of the Year in each of the past two seasons, the first ever back-to-back winner. He was a unanimous first-team All-American selection and was a finalist for the Golden Spikes Award, Howser Award and Pitcher of the Year Award presented by the College Baseball Foundation.
This season in 14 starts, the 21-year-old Boxberger was 6-3 with a 3.16 ERA, 50 walks and 99 strikeouts.
Both players were represented by the same agent, Danny Horwits.
Despite the late announcement, there never appeared to be any danger of the signings not getting done. After the deadline, clubs lose their rights to any unsigned 2009 Draft picks, which go back into the pool to be drafted next year.
Because they weren't expected to pitch much this summer, the Reds didn't move quickly to get Leake and Boxberger into the fold so they could play this season.
"I think we were pretty sure that they would get signed," Buckley said. "We were happy with the deals."