The Cubs announced the deal, which was pending a physical, on Wednesday.
Almora, a Scott Boras client, signed a bonus worth $3.9 million, a source confirmed. The pick's recommended slot value was $3.25 million.
"They knew the player, and they knew the value of the player," Boras said to The Chicago Tribune on Monday, when reports of the agreement surfaced. "With where the Cubs are at, I think the fan base has to believe in player development. So that means these types of signings are very important."
The Cubs have signed 19 of their first 20 picks and 28 players overall who selected in the Draft. Second-rounder Duane Underwood, a high school right-handed pitcher from Georgia, has not signed.
Almora, who had committed to the University of Miami, was considered one of the best all-around position players in the Draft.
The 6-foot-2, 180-pound Almora batted .603 with 13 doubles, five triples, six home runs and 34 RBI in 73 at-bats over 25 games this year for Mater Academy Charter School in Hialeah, Fla. He recorded a 1.164 slugging percentage and a .667 on-base percentage, thanks in part to 14 walks compared to just three strikeouts. Almora, who made the Mater varsity squad as an eighth-grader in 2008, stole 24 bases in 25 attempts.
Almora, who bats and throws right-handed, has an extensive resume with Team USA Baseball. In 2011, he was named USA Baseball's Athlete of the Year after helping the 18-and-under squad go 9-0 and earn the gold medal in the Pan-Am Games, an event in which he was named tournament Most Valuable Player. He has been part of six USA national teams, tied for the most by any player with former Major League catcher A.J. Hinch, and has earned five gold medals.
"I'm speechless," Almora said after being drafted last month. "I don't remember much of anything that happened tonight. I know that the Cubs drafted me and I'm grateful, but I'm still kind of shocked and overwhelmed."