Ledezma was originally signed by the Boston Red Sox as an amateur free agent in 1998. He started his career with the DSL Red Sox in 1998, playing for them one season before joining the GCL Red Sox and the Augusta Greenjackets. He missed the entire 2001 season due to a stress fracture in his left elbow. In 2002, he returned to Augusta but was shut down for the rest of the season on May 22 due to a lower back strain.
Detroit Tigers
Ledezma was drafted by the Detroit Tigers in the 2002 Rule 5 draft on December 16, 2002 and made his Major League debut on April 2, 2003 for the Tigers, working two scoreless innings against the Minnesota Twins. His first win came in a two-inning relief appearance on June 4 against the San Diego Padres. He made his first start on July 8 against the Chicago White Sox. Overall, he was in 34 games during his rookie season and finished 3–7 with a 5.79 ERA. Between 2004 and 2007, he alternated between pitching for the Tigers and for the AA Erie SeaWolves and AAA Toledo Mud Hens. In 2004 with Erie, he was named the Tigers "minor league pitcher of the year" and selected to the Eastern League mid-season all-star team. He pitched in 106 games for Detroit, with a 15–18 record and 5.15 ERA. Ledezma was also the winning pitcher in game 4 of the 2006 American League Championship Series.
Atlanta Braves
Ledezma was traded from the Tigers to the Atlanta Braves for Macay McBride on June 20, 2007. On July 13, 2007, he was placed on the restricted list. He had gone home to Venezuela during the All-Star break, during which he accidentally damaged his visa and passport in the washing machine. The Braves activated him from the restricted list on July 19, 2007. Ledezma was designated for assignment on July 29 by the Braves. He was 0–2 with a 7.71 ERA in 12 appearances for Atlanta. .
San Diego Padres
On July 31, 2007, Ledezma was traded to the San Diego Padres for reliever Royce Ring. He appeared in 9 games with the Padres, with an ERA of 6.28 and also appeared in 11 games for the AAA Portland Beavers, where his ERA was 4.41.
Arizona Diamondbacks
On August 29, 2008, Ledezma was claimed off waivers by the Arizona Diamondbacks and appeared in 3 games for them before he was non-tendered following the season, becoming a free agent.
Washington Nationals
In January 2009, he signed a minor league contract with the Washington Nationals. He appeared in only 5 games for the Nationals, spending most of his time with the Syracuse Chiefs. He was released on July 6, 2009.
On November 30, 2009, Ledezma signed a minor league contract with the Pittsburgh Pirates, with an invite to Spring training. On July 27, 2010, he was called up with Steven Jackson to replace Brad Lincoln and Brendan Donnelly. The Pirates designated Ledezma for assignment on December 24, 2010 to clear roster space after signing free agent pitcher Aaron Thompson. He was in 27 games for the Pirates, with an 0–3 record and 6.86 ERA.
Toronto Blue Jays
On January 5, 2011, Ledezma was claimed off waivers by the Toronto Blue Jays. He began the 2011 season with the Triple-A Las Vegas 51s before having his contract purchased on July 23. Jo-Jo Reyes was designated for assignment to make room on the 40-man roster for Ledezma. Following a 12–0 loss to the Tampa Bay Rays on August 28, Ledezma was designated for assignment. Brian Tallet was called up to replace Ledezma. After the 2011 season, he elected for free agency.
In November 2011, he signed a minor league contract with the Los Angeles Dodgers that contained an invitation to spring training. The Dodgers assigned him to the AAA Albuquerque Isotopes to start the 2012 season. He appeared in 38 games for the Isotopes, with a 3–3 record and 6.99 ERA. He was released on July 24, 2012.
On Demcember 23 2014, he signed a minor league contract with the Minnesota Twins that contained an invitation to spring training. He was released on April 2, 2015.
He was traded to the Rojos del Águila de Veracruz in the middle of the year then became a free agent after the 2016 season. Ledezma later resigned with the club on June 20, 2017. He then became a free agent again following the 2017 season.
