Brennan was born and raised in Redwood City, California, and attended Saint Francis High School in Mountain View, graduating in 1991.

[6] Brennan also had stints as a graduate assistant at Washington under Rick Neuheisel in 1999 and Arizona in 2000 under Dick Tomey.

[13] The 2020 Spartans went 6–0 in the regular season despite having two games canceled and their final two home games relocated due to the COVID-19 pandemic; the pandemic had also forced the team to conduct preseason practices at Humboldt State University due to Santa Clara County restrictions.

[15] Brennan was named the Mountain West Coach of the Year for his team's successes, which included being ranked in the AP Poll for the first time since 2012 and a debut appearance in the College Football Playoff rankings,[16][17] and also finished fifth in the Associated Press College Football Coach of the Year Award voting with three first-place votes.

[21] The 2023 regular season saw the Spartans defeat 25th-ranked Fresno State for their first win over a ranked opponent since 2013, before missing the Mountain West Championship Game via tiebreaker.

[23] On January 16, 2024, Brennan was hired as the head coach at Arizona,[24] signing a five-year contract worth $17.5 million.

[1] Brennan entered his first season with expectations of competing for the Big 12 championship, as the Wildcats were ranked 21st in the AP preseason poll.

[27] Brennan's father Steve played for San Jose State in 1967 while his mother Beth was a cheerleader at the university.