Grichuk, whose mother was unable to get out of jury duty in Texas, agreed to terms on a Minor League contract with his father by his side.
The Angels also signed 20 other players from the Draft, including left-hander Patrick Corbin (second round) and right-hander Danny Reynolds (sixth round).
"We are really excited about Randal signing," director of scouting Eddie Bane said. "We came up with an agreement to everyone's liking and went with it."
Grichuk, 17, of Lamar (Texas) Consolidated High School, played in 28 games in 2009 and hit .613 with 21 home runs and 46 RBIs.
Before the game, Grichuk met with Angels manager Mike Scioscia and the rest of the coaching staff.
"Randal really made a great impression to everyone in the organization," Bane said. "Now, he just has to put in the hard work."
Grichuk will fly Sunday to Arizona, where he will begin playing in the Arizona Rookie League as a left fielder.
With Grichuk signing early after the 2009 First-Year Player Draft, he will also have the opportunity to compete in the Angels' farm system.
"He has great power to right-center, which is quite unusual for a player in high school," Bane said. "He also has quick hands and really uses the entire field."
To some Angels fans, Grichuk's name may sound familiar. He played for Lamar in 2003 and 2004 when it finished fifth and third, respectively, in the Little League World Series.
And for those games, Grichuk quipped, his mother was there.
Left-hander Tyler Kehrer (compensation pick); left-hander Patrick Corbin (second round); right-hander Danny Reynolds (sixth round); infielder Jon Karcich (seventh round); right-hander David Carpenter (ninth round); infielder Dillion Baird (11th round); outfielder Travis Witherspoon (12th round); catcher Jeremy Gillan (17th round); outfielder Daniel Eichelberger (20th round); outfielder Richard Cates (21st round); left-hander Stephen Locke (22nd round); right-hander Taylor Kinzer (24th round); infielder Michael Demperio (25th round); right-hander Carson Andrew (28th round); right-hander Heath Nichols (29th round): outfielder Matt Long (30th round); infielder Eric Oliver (36th round);
infielder Phil Bando (45th round); outfielder Jake Rife (48th round); infielder Alibay Barkley (50th round).