Tejeda will go on the 25-man active roster when he joins the club, possibly on Wednesday. At that time, the Royals will drop a player.
"He's young  and we had several people in our organization who have not only seen him, but know him personally, and felt that he's a guy with more upside," Moore said.
Tejeda, 6-foot-3 and 230 pounds, has seen Major League action in each of the last four seasons. This year he pitched in four games for the Rangers, giving up six runs in six innings. He was designated for assignment June 14.
He spent the first two months this season with Triple-A Oklahoma, going 1-1 with one save and a 2.18 ERA in 10 games, including four starts.
Tejeda broke in with the Philadelphia Phillies in 2005 and went 4-3 with a 3.57 in 26 games, 13 of them starts. That, combined with parts of three seasons with the Rangers, gives him a Major League record of 14-17 and a 5.01 ERA in 63 games (46 starts).
Moore sees Tejeda joining with Ramon Ramirez as a power arm in the bullpen, with Tejeda's fastball reaching about 95 mph. His record shows a high number of bases on balls.
"He's a little erratic," Moore said.
Tejeda played for the Dominican Republic in the inaugural World Baseball Classic and made two relief appearances.
To make room for him on the 40-man roster, the Royals transferred left-hander John Bale to the 60-day disabled list.
Leo Nunez is also on the disabled list, and his loss ultimately triggered several of the recent bullpen moves. He has a strained right lateral muscle, while Bale is recovering from a hand fracture.
"We're hopeful we can get them back after the All-Star break, but they haven't even thrown a pitch in a simulated game, so we don't know," Moore said of his injured relief corps.
Meantime, he said the maneuvers to construct a "perfect" bullpen are likely to continue.
"We've got to be aggressive with our bullpen pitchers and ultimately rely on our scouts' judgments and what they think we need to do, based on the cry for help," Moore said.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.