Marrero was designated for assignment before Tuesday night's game against the New York Yankees.
A major disappointment, Marrero batted just .159 in 32 games with four home runs and nine RBIs. He was acquired from the Atlanta Braves for pitcher Jorge Vasquez on Dec. 16 and was expected to give the Royals right-handed punch. But Marrero hit only .208 against left-handed pitchers.
Costa, 23 and a left-handed hitter, is one of the Royals' rising outfield prospects. For Double-A Wichita, after a slow start, he was hiting .274 with five homers and 27 RBIs.
He was stunned to be called up so soon.
"I did not think that at all. I thought it would probably be a September callup. I was wrong," he said.
"I'm very glad I was wrong. This is a dream come true."
Last season, at the Class A level, Costa finished third in the Carolina League in hitting at .308 and tied for third with 139 hits. He had seven home runs in 451 at-bats for Wilmington and two more in the playoffs, but the Royals feel more power is ahead.
"When he squares up on the ball, he can hit it as hard as anyone we've got," said Shaun McGinn, the Royals' senior director of Minor League operations.
Costa, from Visalia, Calif., twice went to the College World Series with Cal State-Fullerton.
"He's a tough kid. I really like his mental makeup," White said.
Costa was assigned No. 15, worn by Carlos Beltran a year ago.
Royals trivia: Who was the Royals' original manager in 1969? (Answer below.)
Farm report: Infielder Denny Hocking had three hits and knocked in four runs as Triple-A Omaha lost to Albuquerque, 6-5, Monday night. Starting pitcher Dennis Tankersley gave up five runs in 5 2/3 innings.
First baseman Josh Pressley was 3-for-3 with his sixth home run and raised his average to .333, but Wichita lost to Corpus Christi, 10-5. ... Outfielder Mitch Maier hit his league-leading 25th double in Class A High Desert's 7-3 loss to Lancaster. ... Outfielder Alan Moye had three hits and five RBIs as Class A Burlington beat Dayton, 8-3.
Trivia answer: The first Royals manager was Joe Gordon, who had a 69-93 record in the inaugural season -- his only one with the Royals.
On deck: The Royals meet the Yankees in the second of three games at 7:10 p.m. CT Wednesday at Kauffman Stadium. Their challenge: left-hander Randy Johnson, who has a 12-6 career record against them.