Giambrone spent his professional debut season of 2016 with the Eugene Emeralds, hitting .292/.404/.433 with 4 home runs and 22 RBI.[4] He spent the 2017 season with the Myrtle Beach Pelicans, hitting .242/.297/.348 with 12 home runs and 44 RBI.[4] Giambrone spent the 2018 season with the Tennessee Smokies, hitting .251/.333/.440 with 17 home runs and 49 RBI.[6] Following the 2018 season, he played in the Arizona Fall League for the Mesa Solar Sox.[5] Giambrone spent the 2019 season with the Iowa Cubs, hitting .241/.314/.464 with 23 home runs and 66 RBI.[4] He did not play in 2020 due to the cancellation of the Minor League Baseball season because of the COVID-19 pandemic.[7] Assigned back to Iowa for the 2021 minor league season, he hit .174/.274/.255 with 3 home runs and 16 RBI.[8]
On September 29, 2021, Giambrone was selected to the 40-man roster and promoted to the major leagues for the first time. He made his MLB debut that same day.[9] Giambrone went 2-for-13 in 5 games with the Cubs. He was outrighted off of the 40-man roster on November 5.[10]
Giambrone spent the 2022 season back with Iowa. Playing in 89 games, he slashed .188/.281/.270 with 3 home runs, 20 RBI, and 11 stolen bases. He elected free agency following the season on November 10.[11]
On May 27, 2024, Giambrone was traded to the Kansas City Monarchs of the American Association of Professional Baseball in exchange for Jake Cantleberry. In 58 games for the Monarchs, he slashed .298/.366/.445 with seven home runs and 40 RBI. Giambrone was released by Kansas City on August 19.[16]