The 14th overall selection, out of Archbishop McCarthy High School near Fort Lauderdale, Fla., Travieso will receive a bonus of $2 million. According to Major League Baseball guidelines, the recommended bonus slot for that pick is $2.375 million.
The deal for the 18-year-old Travieso is expected to be announced on Wednesday.
A 6-foot-3, 190-pound player, Travieso was 8-1 with a 0.76 ERA this year. He struck out 100 batters and walked 17 in 65 innings. His velocity generally is in the 92-95 mph range, but he reached 99 mph in more recent outings.
Cincinnati also signed its second-round pick, shortstop Tannier Rahier, a high school player out of Indian Wells, Calif., and its third-round pick, right-handed pitcher Daniel Langfield from the University of Memphis. Rahier will receive a $649,700 bonus.
The Reds have signed 16 of their 42 picks from last week's First-Year Player Draft.