He played college football for the Nebraska Cornhuskers and was selected by the Ravens in the sixth round of the 2006 NFL draft.

Koch walked on to the Nebraska football team, where he played punter, and later would receive a scholarship before the start of the 2004 season.

The 2005 average bested the previous record of 45.1 yards per punt by former Bengals punter Kyle Larson in 2003.

[15] A restricted free agent in the 2009 offseason, Koch signed his one-year, $1.545 million tender offer on March 27.

[16][17] After an outstanding 2010 season, Koch was named to the 2010 All-Fundamentals Team by USA Football and the NFL Players Association.

[19] During the 2012 season, Koch scored his first touchdown on a fake field goal in a Week 10 55–20 win over the Oakland Raiders on November 11, 2012.

Koch made key contributions on the final two plays of the Super Bowl, first scrambling in his own end zone to burn time off the clock before taking an elective safety with four seconds remaining.

[24] On July 9, 2015, Koch was re-signed by the Ravens on a five-year, $16.25 million contract, making him one of the highest paid punters in the NFL.

[26] In Week 12 of the 2016 season, against the Cincinnati Bengals, Koch was involved in a strategic maneuver similar to his Super Bowl XLVII play at the end of the game.

With the Ravens leading 19–12 with 11 seconds remaining in the game on their own 23-yard line, Koch fielded the ball and ran back 23 yards to his own endzone to take an intentional safety and run the clock out.

[32] In the 2018 season, Koch had 60 total punts for 2,842 net yards for a 47.37 average, which ranked fourth in the league.

[41] After retiring as a player, Koch joined the Ravens staff as a special teams consultant.