Solis agreed to terms on a $1 million bonus, while Cole received a $2 million bonus.
Solis, a left-handed pitcher, rebounded in 2010 after missing nearly all of the '09 season with a herniated disc in his back, an injury he suffered while lifting weights two years ago. The setback limited the 6-foot-5 lefty to two games that year.
Opting against surgery, he spent an entire summer rehabbing and getting back in shape at Athletes' Performance in Arizona.
All of that hard work eventually paid off when Solis went 9-2 with a 3.42 ERA for the University of San Diego this season. He struck out 92 batters while walking 29 in 92 innings.
"We thought he was a top talent that should have gone higher and we paid him accordingly," assistant general manager Roy Clark said. "We feel he has a chance to move very quickly, and we are very happy to bring him to D.C."
Solis was originally drafted by the D-backs in the 18th round of the 2007 First-Year Player Draft, but instead chose to attend USD.
Cole, a right-hander, joins the Nationals after combining to go 12-1 and fanning 10.7 batters per nine innings during his junior and senior seasons at Oviedo (Fla.) High School. Cole earned All-American status from both AFLAC and Under Armour in 2009.
In the summer of 2007, Cole tossed four scoreless innings for Team USA's Under-16 squad that went 6-0 during the World Youth Championships in Venezuela.
"This is an intense young man. He has a good look about him," said scouting director Kris Kline. "He profiles as a No. 2, front-of-the-line-starter. He may be closer down the road. But he is a starter for now."
Bill Ladson is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.