Koenen attended Ferndale High School in Ferndale, Washington, and was a letterman in football, basketball, and soccer. In football, he won All-Northwest League honors as a senior.
Koenen played college football for Western Washington University in Bellingham, Washington, and is one of only three NFL players to have played football for that school. While there, he received numerous Division II All-American honors from sources such as Street & Smith, Lindy's Football Annuals, Don Hanen's Football Gazette, Daktronics, Inc., and D2football.com, as well as being recognized by the NCAA. He was also named a Great Northwest Athletic Conference (GNAC) all-star four times as a placekicker and twice as a punter. He ended his college career as the Western Washington University, GNAC, and Northwest small college all-time leader in kicking scoring with 272 points, including 43 field goals and 143 PATs. He participated in the 2005 Cactus Bowl.
Koenen signed a two-year free agent contract with the Atlanta Falcons on April 26, 2005. He went on to edge out veteran punter Toby Gowin, who had also signed a free agent deal that offseason, for the starting job with the Falcons. He appeared in all sixteen regular season games for the Falcons, punting 78 times for 3,300 yards, which was good for a 42.3 yards per punt average and ninth in the NFC. He also served as the team's kickoff specialist and was seventh in the NFC in yards per kickoff. His 14 touchbacks put him behind only Pro Bowler Neil Rackers.
In the Falcons' October 9, 2005 game against the New England Patriots, they had the ball on New England's 41 yard line with six seconds remaining in the first half. Since regular placekicker Todd Peterson's range was insufficient to attempt a field goal from that distance, Falcons head coach Jim Mora turned to Koenen. Koenen actually attempted the kick, the first field goal attempt in his pro career, twice. Prior to the initial snap, Patriots linebacker Mike Vrabel called a timeout. Koenen heard the referee's whistle but still kicked the field goal. It landed right of the goalpost. A few moments later, Koenen attempted the kick again, and this time made an official 58 yard field goal. It was the longest field goal of Koenen's career at any level, tied for the ninth longest in NFL history (as well as the single longest in the 2005 season), and was the third longest in history by an undrafted kicker.
In the Falcons' first preseason game of 2006, Koenen made four field goals, from 53, 50, 40, and 45 yards, along with doing the punting and kickoff duties. Koenen was slated to do the placekicking, punting, and kickoffs for the Falcons, something that is rarely done in the NFL by one player; however after he converted only two of eight field goal attempts to start the regular season, the Falcons brought back Morten Andersen, who had kicked in Super Bowl XXXIII for Atlanta eight years earlier, to take over field goal duties. Koenen retained his duties on punts and kickoffs.
During the first game after this change, Koenen was involved in an iconic play. The Falcons visited the New Orleans Saints on Monday Night Football in the first home game for the Saints at the Louisiana Superdome since Hurricane Katrina had devastated the city and the stadium. Koenen's first punt of the game was blocked by Saints safety Steve Gleason. Gleason's block bounced into the end zone and was recovered for a touchdown by Curtis Deloatch. The score put New Orleans up 7-0, a game Atlanta would lose 23-3. The moment was widely considered a moment of revitalization for the city of New Orleans after the hurricane, and a statue of the play was later dedicated outside the Superdome in 2012. Gleason, who was diagnosed with ALS in 2011, and Koenen are both depicted in full on the sculpture. Koenen's name and Falcons logos are absent from the statue, due to the Falcons view that including these marks would be inappropriate, though Koenen later stated that he would not have been opposed to his name being included on the statue if he been approached about it. Koenen also reached out to Gleason on Twitter congratulating him.
For the 2007 season, Koenen returned solely as the Falcons' punter; the club signed Billy Cundiff to handle the other kicking duties. Cundiff was released before the season; Matt Prater was signed but also released after a short while, and the placekicking was again done by Andersen.
A restricted free agent in the 2008 offseason, Koenen was tendered a one-year, $1.417 million contract by the Falcons. He re-signed on April 14.
A free agent in the 2009 offseason, the Falcons placed the franchise tag on Koenen on February 9. He signed the one-year, $2.48 million tender offer on February 13.
Koenen was signed by the Tampa Bay Buccaneers to a six-year, $19.5-million contract on July 29, 2011. Koenen was released at the end of the preseason in September 2015.
Koenen, who majored in general studies, has been married to Devin Koenen since July 14, 2006.