Edwards graduated from Rock Bridge High School in Columbia in 1997 and briefly attended the University of Missouri studying engineering before leaving to focus on racing. He worked as a substitute teacher while pursuing his career. His break came in 2002 when he drove seven Craftsman Truck Series races for MB Motorsports, impressing Jack Roush enough to earn a full-time truck seat for 2003. Running the No. 99 Ford F-150, Edwards won his first race at Kentucky Speedway, took three wins total, and earned Rookie of the Year honors. He added three more truck wins in 2004 before making his Nextel Cup debut at Michigan that August, finishing tenth as a replacement for Jeff Burton.
Edwards joined the Nextel Cup full-time in 2005. On March 19–20 at Atlanta Motor Speedway, he accomplished something no driver had done before: he won both the Busch Series race (the Aaron's 312) and the Nextel Cup race (the Golden Corral 500) in the same weekend, and did so in his first career starts in each series at that event. He closed the season with four Cup wins and third in the standings. He also won the 2005 Busch Series Rookie of the Year award.
After a winless 2006 campaign, Edwards returned to form in 2007. He won at Citizens Bank 400 and at Bristol, clinched a Chase spot, and on November 3 claimed the NASCAR Busch Series championship — the final year the Busch name was used as series sponsor. He finished ninth in Cup points that year.
The 2008 season was Edwards's most prolific in terms of wins: nine Sprint Cup victories including a late-season sweep of wins at Homestead. Despite that total, he lost the championship to Jimmie Johnson by 69 points. Had the points been calculated without the Chase format, Edwards would have won the title by sixteen points based on a fuel strategy decision by crew chief Bob Osborne at Homestead. A post-Las Vegas inspection penalty earlier in the season had cost him 100 driver points, a factor that shaped the championship calculus.
Edwards's most discussed near-championship came in 2011. He entered the season finale at Homestead tied with Tony Stewart on points, but the tiebreaker went to Stewart who had five wins to Edwards's one. Over the course of the Chase, Edwards had raced with remarkable consistency while Stewart made late charges. Had the pre-Chase points system been in place, Edwards would have clinched the title a race early at Phoenix. He re-signed with Roush Fenway that August for a reported $40 million deal.
On the final lap of the 2009 Aaron's 499 at Talladega, Edwards went airborne after contact with Brad Keselowski sent his car backwards into the catch fence. The car was launched by a second impact from Ryan Newman, injuring eight spectators, one of whom required airlift to hospital. Edwards emerged unharmed and jogged across the finish line on foot — drawing a DNF classification despite crossing the line. The incident became one of the most replayed crashes in NASCAR history.
After ten seasons with Roush Fenway, Edwards moved to Joe Gibbs Racing to drive the No. 19 Toyota in 2015. He won the Coca-Cola 600 at Charlotte that year, snapping a 31-race winless streak. In 2016, his final season, he won four Cup races including the Food City 500 at Bristol — leading 276 of 500 laps — and a rain-shortened race at Texas that secured his spot in the Championship 4 at Homestead. In the finale, contact from Joey Logano on a restart ended his last championship bid.
On January 9, 2017, Edwards announced his retirement, stating it was "a pure, simple, personal decision" with no specific next step planned. Daniel Suarez replaced him at JGR for 2017.
Edwards finished his Cup career with 28 wins across 445 starts. He was named among NASCAR's 75 Greatest Drivers in 2023 and inducted into the NASCAR Hall of Fame in 2025. His on-track record features two championship runner-up finishes decided at the final race of the season and a Busch Series title. His cousin is fellow driver Ken Schrader, who advised Edwards early in his career to gain dirt track experience — advice Edwards later credited for his development. Edwards's great-great-great-grandfather was Rutherford B. Hayes, the 19th President of the United States. After retirement, Edwards became an analyst for NASCAR on Prime Video.