Furbush, a native of South Portland, Maine, was the 151st selection of the draft, which began with Rounds 1-5 on Thursday. The draft will continue at 10:30 a.m. CDT Friday with Rounds 6-50.
Detroit's selection of Furbush marked the 20th time in the past 25 seasons an LSU player has been chosen within the first five rounds of the MLB draft.
"I'm very pleased that Charlie was selected by an outstanding organization like the Detroit Tigers," said LSU coach Paul Mainieri. "He came to LSU because he wanted the challenge of facing the best competition in the country, and I'm happy we helped him realize that goal. He was a valuable member of our staff this season, and we will support any decision that he and his family make as it relates to his baseball future."
Furbush, who transferred to LSU last fall from Saint Joseph's (Maine) College, posted a 3-9 mark for the Tigers in 2007 with a 4.95 ERA and 88 strikeouts in 87.1 innings.
Furbush defeated Saint Mary's (Calif.) in his LSU debut on February 9, allowing no runs on five hits in 5.2 innings with three walks and seven strikeouts. He worked a season-high eight innings in a win over Southern Mississippi on March 9, allowing one unearned run on three hits with no walks and five strikeouts.
Furbush recorded 10 strikeouts on two occasions - at South Carolina on March 16 and at Alabama on March 30.
Furbush was the No. 1 left-handed pitching prospect in the prestigious Cape Cod League in 2006, and he was ranked as the 10th-best overall prospect in the CCL by Baseball America magazine.
He received the CCL John Claffey New England Top Prospect Award in 2006 after posting a 3-2 record with a 1.83 ERA in 54 innings of work. He started seven games, struck out 50 hitters and limited opponents to a .212 batting average.
Tigers Furbush taken in 4th round
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