Tate attended Robert E. Lee High School in Baytown, Texas, where he was coached there by his stepfather Dick Olin and had a record breaking career. He ranks first in the Texas high school football record book in career pass attempts and completions, ahead of Graham Harrell. He also ranks second in career passing yards with 12,183, behind Harrell, and third in career touchdown passes with 113, behind Harrell and Colt McCoy. He originally committed to Texas A&M, but de-committed after R. C. Slocum was replaced with Dennis Franchione. Tate also noted that he would likely sit behind established starter Reggie McNeal, so he chose to play for the University of Iowa under coach Kirk Ferentz. He played in the 2003 U.S. Army All-American Bowl.
At a game well-attended by Iowa fans in Orlando, Florida, the Hawkeye defense played strong against the LSUoffense. However, LSU took their first lead with 46 seconds remaining. On the game’s final play, Tate attained fame when he threw a 56-yard, game-winning touchdown pass to senior Warren Holloway as time expired. This was Holloway's only touchdown at Iowa. Many Iowa fans say this was the greatest play in the school's football history.
Honors
2004 All-Big Ten Conference First Team and Second Team
On May 3, 2007, Tate signed with the St. Louis Rams as a free agent, but he became expendable after the Rams signed Brock Berlin. Tate was released on May 22, 2007.
Saskatchewan Roughriders
After his release from the Rams, Tate signed a practice roster agreement with the Saskatchewan Roughriders in 2007. After spending two years on either the practice roster or the injured reserve list, Tate was removed from the practice roster on November 9, 2008 and became a free agent.
Calgary Stampeders
Tate signed with the Calgary Stampeders on June 3, 2009. On November 9, 2010, Tate signed a contract extension with the Stampeders. Due to ineffective play by incumbent quarterback Henry Burris, Tate received his first professional start against his former team, the Roughriders, on October 22, 2011 and posted a 25–13 win. Tate went on to lead the Stampeders to three straight wins to the finish off the regular season. Drew Tate made his first CFL Playoff start against the Edmonton Eskimos. Tate struggled throwing 5 completions in 10 attempts for 99 yards and an interception. At the start of the second half he was replaced by Henry Burris who could not lead the Stamps to victory, thus ending the season. In the off-season the Stamps traded away Burris making Tate the starting quarterback. He opened the 2012 CFL season with a dominant win over the Montreal Alouettes. However, in the second week of the season Tate suffered a dislocated shoulder in his non-throwing arm. Tate opted to perform surgery on it immediately, seemingly ending his season. However, Tate returned to play in the final two games of the regular season. Tate was announced the starter for Stamps home game of the Western Division Semi-Finals against the Saskatchewan Roughriders. He broke his forearm and may have suffered a concussion during the game but played the entire game nonetheless. His 68-yard TD pass to Romby Bryant with only 20 seconds left gave the Stamps the victory. However, the broken forearm would cause him to miss the Western Final and the 100th Grey Cup. In Week 2 of the 2013 CFL season Tate could not finish the game after straining a forearm muscle in his throwing arm early in the game. Tate confessed to feeling pain in the same muscle in the month prior to the injury but played through the pre-season and majority of the first 2 weeks. Tate was listed as day-to-day and did not start Week 3 against the Montreal Alouettes; his back-up QB Kevin Glenn played in his place. Tate was expected to return to the starting position for Week 7, however, he suffered a setback to his throwing arm in practice leading up to the August 9th game. On August 8 it was announced that Tate would miss an additional 2–3 weeks. Coach Hufnagel compared the injury to tennis elbow. Tate finished the 2013 season having only played in 7 games due to various injuries. In the off-season starting quarterback Kevin Glenn was selected by the Ottawa RedBlacks in the Expansion Draft. On January 14, 2014 Tate was signed to a contract extension. Tate was primarily used in short yardage situations and led the CFL in rushing touchdowns during the 2014 season with ten scores as the backup to Bo Levi Mitchell. He scored two one-yard rushing touchdowns in the Stampeders' 20–16 victory over the Hamilton Tiger-Cats in the 102nd Grey Cup. As a passer Tate attempted his second most passes in a single season with 111, completing a career low of only 59.5% of them. Less than one month prior to becoming a free-agent Drew Tate and the Stampeders agreed to a contract extension. Tate continued as the Stamps backup quarterback behind Bo Levi Mitchell for the 2015 and 2016 seasons; starting in only 1 game each season to rest Mitchell for the playoffs.
On November 3, 2018, the final day of the 2018 regular season, Tate came out of retirement to join the Saskatchewan Roughriders, the team he started his CFL career with ten years prior. On December 17, 2018, Tate announced he was retiring from the Canadian Football League.
